login
A354746
Non-repdigit numbers k such that every permutation of the digits of k has the same number of distinct prime divisors.
2
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
KEYWORD
nonn,base
AUTHOR
Metin Sariyar, Jun 05 2022
STATUS
approved