A387364 Least number which is not a prime power and whose prime factors are equal modulo n.

6, 15, 10, 21, 14, 55, 46, 33, 22, 39, 26, 85, 82, 51, 34, 57, 38, 115, 118, 69, 46, 141, 142, 145, 159, 87, 58, 93, 62, 259, 314, 185, 202, 111, 74, 205, 226, 123, 82, 129, 86, 235, 262, 141, 94, 371, 291, 265, 298, 159, 106, 321, 327, 295, 334, 177, 118, 183

Offset: 1

Author

Yaroslav Deryavko, Aug 27 2025

Keywords

• nonn
• new

Examples

			For n = 2, factors of a(2) = 15 are 3 and 5, they both have a residue of 1 mod 2.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Crossrefs

First term of A380758 when n = 10.

Programs

Mathematica

a[n_]:=Module[{k=1},Until[!PrimePowerQ[k]&&Min[Mod[First/@FactorInteger[k],n]]==Max[Mod[First/@FactorInteger[k],n]],k++];k];Array[a,58] (* James C. McMahon, Sep 03 2025 *)

PARI

f(k, n) = if (!isprimepower(k), my(f=factor(k)[,1]); #Set(apply(x->Mod(x, n), f)) == 1);
a(n) = my(k=1); while (!f(k,n), k++); k; \\ Michel Marcus, Aug 27 2025