A389216 Nonsquarefree numbers k such that {sum of unitary divisors of k} plus {sum of squarefree divisors of k} >= 2*k.

4, 12, 18, 20, 24, 28, 44, 52, 60, 68, 76, 84, 90, 92, 116, 120, 124, 126, 132, 140, 148, 150, 156, 164, 168, 172, 180, 188, 198, 204, 212, 220, 228, 234, 236, 240, 244, 260, 264, 268, 270, 276, 280, 284, 292, 294, 306, 308, 312, 315, 316, 332, 340, 342, 348, 350, 356, 364, 372, 378, 380, 388, 404, 408, 412, 414

Offset

1,1

Comments

Terms k of A013929 for which A325973(k) >= k, or equally, A325977(k) >= 0.

Apparently A363082 is a subsequence. After 4, the next terms not occurring in it are a(36)=240 and a(41)=270.

Links

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

Formula

{k | A008683(k) = 0 and A034448(k)+A048250(k) >= 2*k}.

Prog

(PARI)
A325973(n) = (1/2)*sumdiv(n, d, d*(issquarefree(d) + (1==gcd(d, n/d))));
is_A389216(k) = (!issquarefree(k) && (A325973(k) >= k));

Crossrefs

Intersection of A013929 and A389215.

Cf. A008683, A034448, A048250, A325973, A325977.

Subsequences: A325963\{1}, A363082 (conjectured), A389079 (odd terms).

Sequence in context: A350602 A362873 A111371 * A078514 A324519 A381953

Adjacent sequences: A389213 A389214 A389215 * A389217 A389218 A389219

Keyword

nonn

Author

Antti Karttunen, Sep 30 2025

Status

approved