A354745 Non-repdigit numbers k such that every permutation of the digits of k has the same number of divisors.

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

Author

Metin Sariyar, Jun 05 2022

Keywords

• nonn
• base

Comments

After a(93) = 84444, no further terms < 10^18. - Michael S. Branicky, Jun 08 2022

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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

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