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A354745
Non-repdigit numbers k such that every permutation of the digits of k has the same number of divisors.
1
13, 15, 17, 24, 26, 31, 37, 39, 42, 51, 58, 62, 71, 73, 79, 85, 93, 97, 113, 117, 131, 155, 171, 177, 178, 187, 199, 226, 262, 288, 311, 337, 339, 355, 373, 393, 515, 535, 551, 553, 558, 585, 622, 711, 717, 718, 733, 771, 781, 817, 828, 855, 871, 882, 899, 919, 933, 989, 991, 998
OFFSET
1,1
COMMENTS
After a(93) = 84444, no further terms < 10^18. - Michael S. Branicky, Jun 08 2022
EXAMPLE
871 is a term because d(871) = d(817) = d(178) = d(187) = d(718) = d(781) = 4, where d(n) is the number of divisors of n.
MATHEMATICA
Select[Range[10000], CountDistinct[DivisorSigma[0, FromDigits /@ Permutations[IntegerDigits[#]]]]==1&&CountDistinct[IntegerDigits[#]]>1&]
PROG
(Python)
from sympy import divisor_count
from itertools import permutations
def ok(n):
s, d = str(n), divisor_count(n)
if len(set(s)) == 1: return False
return all(d==divisor_count(int("".join(p))) for p in permutations(s))
print([k for k in range(5500) if ok(k)]) # Michael S. Branicky, Jun 05 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Metin Sariyar, Jun 05 2022
STATUS
approved