A115662 -id:A115662 - cp's OEIS frontend

A115661 Numbers n which have the same number of distinct prime divisors as the reverse of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 21, 22, 23, 26, 28, 31, 32, 33, 36, 37, 39, 44, 45, 51, 54, 55, 56, 57, 58, 61, 62, 63, 65, 66, 68, 69, 71, 73, 75, 77, 79, 82, 85, 86, 88, 93, 96, 97, 99, 101, 107, 108, 111, 113, 115, 116, 117, 121, 122, 123, 125, 128

Offset: 1

Giovanni Resta, Jan 29 2006

			omega(16)=omega(61)=1.

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A001221, A115662.

Select[Range[130],PrimeNu[#]==PrimeNu[FromDigits[Reverse[ IntegerDigits[ #]]]]&] (* Harvey P. Dale, Jan 14 2012 *)

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

Original entry on oeis.org

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

Metin Sariyar, Jun 05 2022

			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.

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

Cf. A001221, A003459, A115662, A354745.

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

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

cp's OEIS Frontend

A115661 Numbers n which have the same number of distinct prime divisors as the reverse of n.

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