A389211 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.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 98

Offset

1,2

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

A389211Q[k_] := MoebiusMu[k] != 0 || (2*DivisorSigma[1, k] - (Times @@ (Power @@@ # + 1) + Times @@ (#[[All, 1]] + 1)) <= 2*k & [FactorInteger[k]]);
Select[Range[200], A389211Q] (* Paolo Xausa, Oct 14 2025 *)

Prog

(PARI)
A325974(n) = (1/2)*sumdiv(n, d, d*((1-issquarefree(d))+(gcd(d, n/d)>1)));
is_A389211(k) = (A325974(k) <= k);

Crossrefs

Positions of nonnegative terms in A325978.

Cf. A034448, A048146, A162296, A325974, A389212 (complement).

Subsequences: A005117, A389213.

Sequence in context: A380693 A043093 A023802 * A007915 A377019 A344742

Adjacent sequences: A389208 A389209 A389210 * A389212 A389213 A389214

Keyword

nonn

Author

Antti Karttunen, Sep 30 2025

Status

approved