A354746 Non-repdigit numbers k such that every permutation of the digits of k has the same number of distinct prime divisors.

12, 13, 15, 16, 17, 21, 23, 26, 28, 31, 32, 36, 37, 39, 45, 51, 54, 56, 57, 58, 61, 62, 63, 65, 68, 69, 71, 73, 75, 79, 82, 85, 86, 93, 96, 97, 113, 116, 117, 122, 131, 155, 156, 161, 165, 171, 177, 178, 187, 199, 212, 221, 224, 226, 228, 242, 245, 248, 254, 255, 258, 262, 282

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..217

Example

156 is a term because omega(156) = omega(165) = omega (516) = omega(561) = omega(615) = omega(651) = 3, where omega(n) is the number of distinct prime divisors of n.

Mathematica

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

Prog

(Python)
from sympy import factorint
from itertools import permutations
def ok(n):
    s, pf = str(n), len(factorint(n))
    if len(set(s)) == 1: return False
    return all(pf==len(factorint(int("".join(p)))) for p in permutations(s))
print([k for k in range(500) if ok(k)]) # Michael S. Branicky, Jun 05 2022

Crossrefs

Cf. A001221, A003459, A115662, A354745.

Sequence in context: A308919 A048026 A115662 * A136200 A096514 A074163

Adjacent sequences: A354743 A354744 A354745 * A354747 A354748 A354749

Keyword

nonn,base

Author

Metin Sariyar, Jun 05 2022

Status

approved