A086368 Nonsquarefree numbers k such that sigma(k) is squarefree.

4, 8, 9, 16, 18, 20, 25, 36, 45, 49, 50, 64, 72, 80, 100, 104, 116, 117, 121, 128, 144, 148, 169, 180, 196, 200, 208, 225, 234, 242, 244, 256, 261, 289, 292, 296, 320, 325, 333, 361, 369, 404, 436, 441, 450, 452, 464, 488, 512, 529, 548, 549, 576, 578, 584, 592

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

k = 45 = 3*3*5 and sigma(45) = 78 = 2*3*13.

Maple

filter:= n -> not numtheory:-issqrfree(n) and numtheory:-issqrfree(numtheory:-sigma(n)):
select(filter, [$1..1000]); # Robert Israel, May 11 2018

Mathematica

q[k_] := ! SquareFreeQ[k] && SquareFreeQ[DivisorSigma[1, k]]; Select[Range[600], q] (* Amiram Eldar, Feb 24 2025 *)

Prog

(PARI) isok(k) = !issquarefree(k) && issquarefree(sigma(k)); \\ Amiram Eldar, Feb 24 2025

Crossrefs

Intersection of A013929 and A065300.

Cf. A000203 (sigma), A005117, A065303, A087249, A065301.

Sequence in context: A140612 A225353 A034023 * A034024 A370354 A375403

Adjacent sequences: A086365 A086366 A086367 * A086369 A086370 A086371

Keyword

nonn,changed

Author

Labos Elemer, Sep 05 2003

Status

approved