def find_sum(self, limit, modulo=(2 ** 32)):
out = 0
self.limit = limit
self.primes = mylib.make_primes_sieve_atkin(limit)
print('found', len(self.primes), 'primes')
not_hamming = self.make_sieve()
return (int((self.limit * (self.limit + 1)) // 2) - sum(not_hamming)) % modulo
def find_sum(self, limit, modulo=(2**32)):
out = 0
self.limit = limit
self.primes = mylib.make_primes_sieve_atkin(limit)
print('found', len(self.primes), 'primes')
not_hamming = self.make_sieve()
return (int(
(self.limit * (self.limit + 1)) // 2) - sum(not_hamming)) % modulo
def sigma2(self, n):
r = math.floor(n ** 0.5)
pp = mylib.make_primes_sieve_atkin(n)
modulo_plus = self.modulo * 10
nm = n % modulo_plus
out = ((nm - 1) + int((nm * (nm + 1) * (2 * nm + 1) / 6))) % self.modulo
for p in pp:
k = n // p
pm = p % self.modulo
out = (out + (pm ** 2) * (k - 1)) % self.modulo
print(p, '/', n, out)
print(out)
return out
def test(self):
p = 4
self.pp = mylib.make_primes_sieve_atkin(10 ** p)
self.make_right_harshads(p - 1).filter_strong().make_primes()
for hh in self.hhh:
print(hh)
print(self.ss)
print(sum(self.rr), 90619 - sum(self.rr), self.rr)
# h = Harshad(3608528850368400786036725)
# print(h, h.is_harshad, h.is_right())
# print(len(pp), sum(len(hh) for hh in self.hhh))
# print(pp)
# print(self.hhh)
return False
def sigma2(self, n):
r = math.floor(n**0.5)
pp = mylib.make_primes_sieve_atkin(n)
modulo_plus = self.modulo * 10
nm = n % modulo_plus
out = ((nm - 1) + int(
(nm * (nm + 1) * (2 * nm + 1) / 6))) % self.modulo
for p in pp:
k = n // p
pm = p % self.modulo
out = (out + (pm**2) * (k - 1)) % self.modulo
print(p, '/', n, out)
print(out)
return out
def find_triplets(self):
# self.triplets = []
pp = mylib.make_primes_sieve_atkin(self.limit)
bb = dict()
r = int(self.limit**0.5 // 1)
ss = [x**2 for x in pp if x < r]
print(len(pp), "primes, last 10:", sorted(pp)[-10:])
print(len(ss), "squares, last 10:", ss[-10:], "\n")
for a in pp:
print("\033[F\033[K", a, "filtering")
a1 = a + 1
for s in ss:
if s > a1:
bb[a] = (a1, 1)
break
if not a1 % s:
b = a1 // s
if (b - 1) in bb and bb[b - 1][0] != b:
bb[a] = (bb[b - 1][0], a1 // b * bb[b - 1][1])
else:
bb[a] = (b, a1 // b)
break
else:
bb[a] = (a1, 1)
continue
_aaa = dict()
for a in bb:
print("\033[F\033[K", a, 'combining')
b = bb[a][0]
if b not in _aaa:
_aaa[b] = dict()
_aaa[b][a] = round(bb[a][1]**(1 / 2))
aaa = dict()
n = 0
for b in _aaa:
l = len(_aaa[b])
if l > 1:
print("\033[F\033[K", b, "use elements with len > 1:", l)
aaa[b] = _aaa[b]
n += l * (l - 1) // 2
# else:
# print("\033[F\033[K", k, "remove elements with len = 1")
k = len(aaa)
print("TOTAL", k, "keys to iterate")
print("TOTAL", n, "iterations\n")
bb = sorted(aaa.keys())
k1 = 0
n1 = 0
for b in bb:
k1 += 1
aa = aaa[b]
rr = sorted(aa.keys())
l = len(rr)
print(k1, "/", k, ":", b, l, rr, "\n")
for i in range(0, l):
for j in range(i + 1, l):
n1 += 1
p = rr[i]
q = rr[j]
r = b * aa[p] * aa[q] - 1
if r not in pp:
continue
t = (p, r, q)
self.triplets.append(t)
print("\033[F\033[K", n1, "/", n, t, len(self.triplets))
return self
import mylib, sys
L = 10 ** 2
pp = mylib.make_primes_sieve_atkin(L)
def my_fact2(p):
out = 1
if p < 10:
for x in range(1, p - 4):
out = (out * x) % p
return out
out = 24 % p
for x in range(5, (p + 1) // 2):
out = (((p - out) * x) % p * x) % p
return out
def s3(p):
return (my_fact2(p) * 9) % p
sigma = 0
for a in pp:
if a < 5:
continue
sa = s3(a)
sigma += sa
print("\033[F\033[K", end="")
print(a, sa)
print(sigma)
def find_triplets(self):
# self.triplets = []
pp = mylib.make_primes_sieve_atkin(self.limit)
bb = dict()
r = int(self.limit ** 0.5 // 1)
ss = [x ** 2 for x in pp if x < r]
print(len(pp), "primes, last 10:", sorted(pp)[-10:])
print(len(ss), "squares, last 10:", ss[-10:], "\n")
for a in pp:
print("\033[F\033[K", a, "filtering")
a1 = a + 1
for s in ss:
if s > a1:
bb[a] = (a1, 1)
break
if not a1 % s:
b = a1 // s
if (b - 1) in bb and bb[b - 1][0] != b:
bb[a] = (bb[b - 1][0], a1 // b * bb[b - 1][1])
else:
bb[a] = (b, a1 // b)
break
else:
bb[a] = (a1, 1)
continue
_aaa = dict()
for a in bb:
print("\033[F\033[K", a, 'combining')
b = bb[a][0]
if b not in _aaa:
_aaa[b] = dict()
_aaa[b][a] = round(bb[a][1] ** (1 / 2))
aaa = dict()
n = 0
for b in _aaa:
l = len(_aaa[b])
if l > 1:
print("\033[F\033[K", b, "use elements with len > 1:", l)
aaa[b] = _aaa[b]
n += l * (l - 1) // 2
# else:
# print("\033[F\033[K", k, "remove elements with len = 1")
k = len(aaa)
print("TOTAL", k, "keys to iterate")
print("TOTAL", n, "iterations\n")
bb = sorted(aaa.keys())
k1 = 0
n1 = 0
for b in bb:
k1 += 1
aa = aaa[b]
rr = sorted(aa.keys())
l = len(rr)
print(k1, "/", k, ":", b, l, rr, "\n")
for i in range(0, l):
for j in range(i + 1, l):
n1 += 1
p = rr[i]
q = rr[j]
r = b * aa[p] * aa[q] - 1
if r not in pp:
continue
t = (p, r, q)
self.triplets.append(t)
print("\033[F\033[K", n1, "/", n, t, len(self.triplets))
return self
import mylib
primes = mylib.make_primes_sieve_atkin(10 ** 4) # a ** b means a in power of b, in this case 10000
harshads_by_power_of_ten = list()
harshads_by_power_of_ten.append([]) # append ~ push a new element in the list
harshads_by_power_of_ten.append([1, 2, 3, 4, 5, 6, 7, 8, 9])
def make_right_harshads(power_of_ten):
if len(harshads_by_power_of_ten) < power_of_ten:
make_right_harshads(power_of_ten - 1)
previous_harshads = harshads_by_power_of_ten[power_of_ten - 1]
harshads_new = []
for harshad_number in previous_harshads:
harshads_new += gen_next_right_harshads(power_of_ten, harshad_number)
harshads_by_power_of_ten.append(harshads_new)
print('-' * 79)
def gen_next_right_harshads(power_of_ten, previous_harshad_number):
out = list()
new_base = 10 * previous_harshad_number
remainder = new_base % power_of_ten
if not remainder:
out.append(new_base) # add 20, 240, 3240 etc
for x in range(power_of_ten - remainder, 10, power_of_ten): # ~ for (i=p-r; i<10; i+=p)
out.append(new_base + x)
# for example, for 220, cycle goes through 3-1 = 2, 5, 8 and we store 222, 225, 228
print(power_of_ten, previous_harshad_number, out)
return out
import mylib
primes = mylib.make_primes_sieve_atkin(
10**4) # a ** b means a in power of b, in this case 10000
harshads_by_power_of_ten = list()
harshads_by_power_of_ten.append([]) # append ~ push a new element in the list
harshads_by_power_of_ten.append([1, 2, 3, 4, 5, 6, 7, 8, 9])
def make_right_harshads(power_of_ten):
if len(harshads_by_power_of_ten) < power_of_ten:
make_right_harshads(power_of_ten - 1)
previous_harshads = harshads_by_power_of_ten[power_of_ten - 1]
harshads_new = []
for harshad_number in previous_harshads:
harshads_new += gen_next_right_harshads(power_of_ten, harshad_number)
harshads_by_power_of_ten.append(harshads_new)
print('-' * 79)
def gen_next_right_harshads(power_of_ten, previous_harshad_number):
out = list()
new_base = 10 * previous_harshad_number
remainder = new_base % power_of_ten
if not remainder:
out.append(new_base) # add 20, 240, 3240 etc
for x in range(power_of_ten - remainder, 10,
power_of_ten): # ~ for (i=p-r; i<10; i+=p)
out.append(new_base + x)
# for example, for 220, cycle goes through 3-1 = 2, 5, 8 and we store 222, 225, 228
