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

1,1

Comments

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

Links

Table of n, a(n) for n=1..60.

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

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

Sequence in context: A031060 A120129 A350867 * A341329 A109019 A068893

Adjacent sequences: A354742 A354743 A354744 * A354746 A354747 A354748

Keyword

nonn,base

Author

Metin Sariyar, Jun 05 2022

Status

approved