A392815 Numbers k for which A392814(k) > 0.

8, 9, 16, 18, 24, 25, 32, 36, 40, 45, 48, 49, 50, 56, 63, 64, 72, 75, 80, 81, 88, 90, 96, 98, 99, 100, 104, 112, 117, 120, 121, 125, 126, 128, 136, 144, 147, 150, 152, 153, 160, 162, 168, 169, 171, 175, 176, 180, 184, 192, 196, 198, 200, 207, 208, 216, 224, 225, 232, 234, 240

Offset

1,1

Comments

All the terms are nonsquarefree numbers since A392814(k) = 0 for a squarefree number k.

Numbers whose prime factorization includes at least one prime power, p^e, such that p mod e > 0 (i.e., 1 < e != p).

The asymptotic density of this sequence is 1 - Product_{p prime} (1 - 1/p^2 + 1/p^p - 1/p^(p+1)) = 1 - (1/zeta(2)) * Product_{p prime} (1 + 1/((p+1)*p^(p-1))) = 0.27085521196763521798... .

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

f[p_, e_] := Mod[p, e]; q[1] = False; q[k_] := Plus @@ f @@@ FactorInteger[k] > 0; Select[Range[240], q]

Prog

(PARI) isok(k) = {my(f = factor(k)); sum(i = 1, #f~, f[i, 1] % f[i, 2]) > 0; }

Crossrefs

Subsequence of A013929.

Cf. A005117, A013661, A392814.

Sequence in context: A236300 A046790 A057111 * A171425 A143720 A231016

Adjacent sequences: A392812 A392813 A392814 * A392816 A392817 A392818

Keyword

nonn,easy

Author

Amiram Eldar, Jan 24 2026

Status

approved