A389210 Positions of odd terms in A325974, where A325974 is the arithmetic mean of {sum of non-unitary divisors} and {sum of nonsquarefree divisors}.

4, 8, 16, 25, 32, 50, 64, 100, 128, 169, 200, 225, 256, 289, 338, 400, 441, 450, 512, 578, 625, 676, 800, 841, 882, 900, 1024, 1089, 1156, 1225, 1250, 1352, 1369, 1521, 1600, 1681, 1682, 1764, 1800, 2025, 2048, 2178, 2312, 2450, 2500, 2601, 2704, 2738, 2809, 3025, 3042, 3200, 3249, 3362, 3364, 3528, 3600, 3721

Offset

1,1

Links

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

Mathematica

A389210Q[k_] := MoebiusMu[k] == 0 && (OddQ[DivisorSigma[1, k] - (Times @@ (Power @@@ # + 1) + Times @@ (#[[All, 1]] + 1))/2 & [FactorInteger[k]]]);
Select[Range[5000], A389210Q] (* Paolo Xausa, Oct 14 2025 *)

Prog

(PARI)
A325974(n) = (1/2)*sumdiv(n, d, d*((1-issquarefree(d))+(gcd(d, n/d)>1)));
is_A389210(k) = (A325974(k)%2);

Crossrefs

Setwise difference A028982 \ A389205.

Cf. A048146, A162296, A325974.

Cf. also A069562.

Sequence in context: A246067 A378250 A161226 * A369566 A022560 A290190

Adjacent sequences: A389207 A389208 A389209 * A389211 A389212 A389213

Keyword

nonn

Author

Antti Karttunen, Oct 06 2025

Status

approved