A325814 a(n) = n - A048146(n), where A048146 is the sum of non-unitary divisors of n.

1, 2, 3, 2, 5, 6, 7, 2, 6, 10, 11, 4, 13, 14, 15, 2, 17, 9, 19, 8, 21, 22, 23, 0, 20, 26, 15, 12, 29, 30, 31, 2, 33, 34, 35, -5, 37, 38, 39, 4, 41, 42, 43, 20, 27, 46, 47, -8, 42, 35, 51, 24, 53, 18, 55, 8, 57, 58, 59, 12, 61, 62, 39, 2, 65, 66, 67, 32, 69, 70, 71, -33, 73, 74, 55, 36, 77, 78, 79, -4, 42, 82, 83, 20

Offset: 1

Author

Antti Karttunen, May 23 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000203, A033879, A034448, A034460, A048146, A064591 (positions of zeros), A228058, A325812, A325813, A325824.

Cf. also A325314.

Cf. A002117, A013661.

Programs

Mathematica

Table[n - DivisorSum[n, # &, ! CoprimeQ[#, n/#] &], {n, 84}] (* Michael De Vlieger, May 27 2019 *)

PARI

A048146(n) = (sigma(n)-A034448(n));
A325814(n) = (n-A048146(n));

Formula

a(n) = n - A048146(n).

a(n) = A033879(n) + A034460(n).

a(A228058(n)) = A325824(n).

Sum_{k=1..n} a(k) ~ c * n^2, where c = 1/2 - zeta(2) * (1 - 1/zeta(3)) / 2 = 0.3617493553... . - Amiram Eldar, Feb 22 2024