A389212 Numbers k such that A048146(k)+A162296(k) > 2*k, where A048146 is the sum of non-unitary divisors of n, and A162296 is the sum of divisors of n that have a square factor.

8, 16, 24, 32, 36, 40, 48, 54, 56, 60, 64, 72, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 135, 136, 140, 144, 150, 152, 156, 160, 162, 168, 176, 180, 184, 189, 192, 196, 198, 200, 204, 208, 216, 224, 225, 228, 232, 234, 240, 248, 250, 252, 256, 264, 270, 272, 276, 280, 288, 294, 296, 300, 304, 306

Offset

1,1

Comments

Numbers k for which A325974(k) > k, or equally, A325978(k) < 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Mathematica

A389212Q[k_] := MoebiusMu[k] == 0 && (2*DivisorSigma[1, k] - (Times @@ (Power @@@ # + 1) + Times @@ (#[[All, 1]] + 1)) > 2*k & [FactorInteger[k]]);
Select[Range[300], A389212Q] (* Paolo Xausa, Oct 14 2025 *)

Prog

(PARI)
A325974(n) = (1/2)*sumdiv(n, d, d*((1-issquarefree(d))+(gcd(d, n/d)>1)));
is_A389212(k) = (A325974(k) > k);

Crossrefs

Positions of negative terms in A325978.

Subsequence of A013929 and of A389214.

Cf. A034448, A048146, A162296, A325974, A389211 (complement).

Cf. also A289554, which is not a subsequence: 210, 220, 243 are its first three terms not included in this sequence.

Sequence in context: A386944 A344538 A244371 * A144566 A037989 A044848

Adjacent sequences: A389209 A389210 A389211 * A389213 A389214 A389215

Keyword

nonn

Author

Antti Karttunen, Sep 30 2025

Status

approved