A325314 a(n) = n - A162296(n), where A162296(n) is the sum of divisors of n that have a square factor.

1, 2, 3, 0, 5, 6, 7, -4, 0, 10, 11, -4, 13, 14, 15, -12, 17, -9, 19, -4, 21, 22, 23, -24, 0, 26, -9, -4, 29, 30, 31, -28, 33, 34, 35, -43, 37, 38, 39, -32, 41, 42, 43, -4, -9, 46, 47, -64, 0, -25, 51, -4, 53, -54, 55, -40, 57, 58, 59, -36, 61, 62, -9, -60, 65, 66, 67, -4, 69, 70, 71, -111, 73, 74, -25, -4, 77, 78, 79, -88, -36, 82, 83

Offset: 1

Author

Antti Karttunen, Apr 21 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A013661, A033879, A162296, A228058, A325313, A325315, A325320.

Programs

Mathematica

Array[# - DivisorSigma[1, #] + Times @@ (1 + FactorInteger[#][[;; , 1]]) - Boole[# == 1] &, 83] (* Michael De Vlieger, Jun 06 2019, after Amiram Eldar at A162296 *)

PARI

A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
A325314(n) = (n - A162296(n));

Formula

a(n) = n - A162296(n).

a(n) = A033879(n) + A325313(n).

a(A228058(n)) = -A325320(n).

Sum_{k=1..n} a(k) ~ c * n^2, where c = 1 - zeta(2)/2 = 0.1775329665... . - Amiram Eldar, Feb 22 2024