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
Examples
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.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..217
Programs
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Mathematica
Select[Range[10000],CountDistinct[PrimeNu[FromDigits /@ Permutations[IntegerDigits[#]]]]==1&&CountDistinct[IntegerDigits[#]]>1&]
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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