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Non-repdigit numbers k such that every permutation of the digits of k has the same number of divisors.
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%I #27 Jun 09 2022 02:25:38

%S 13,15,17,24,26,31,37,39,42,51,58,62,71,73,79,85,93,97,113,117,131,

%T 155,171,177,178,187,199,226,262,288,311,337,339,355,373,393,515,535,

%U 551,553,558,585,622,711,717,718,733,771,781,817,828,855,871,882,899,919,933,989,991,998

%N Non-repdigit numbers k such that every permutation of the digits of k has the same number of divisors.

%C After a(93) = 84444, no further terms < 10^18. - _Michael S. Branicky_, Jun 08 2022

%e 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.

%t Select[Range[10000],CountDistinct[DivisorSigma[0,FromDigits /@ Permutations[IntegerDigits[#]]]]==1&&CountDistinct[IntegerDigits[#]]>1&]

%o (Python)

%o from sympy import divisor_count

%o from itertools import permutations

%o def ok(n):

%o s, d = str(n), divisor_count(n)

%o if len(set(s)) == 1: return False

%o return all(d==divisor_count(int("".join(p))) for p in permutations(s))

%o print([k for k in range(5500) if ok(k)]) # _Michael S. Branicky_, Jun 05 2022

%Y Cf. A000005, A003459, A067012, A062895, A350867, A354746.

%K nonn,base

%O 1,1

%A _Metin Sariyar_, Jun 05 2022