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

1,2

Links

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

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

Mathematica

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

Prog

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

Crossrefs

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

Cf. also A325314.

Cf. A002117, A013661.

Sequence in context: A304768 A243057 A090078 * A325126 A377515 A327937

Adjacent sequences: A325811 A325812 A325813 * A325815 A325816 A325817

Keyword

sign

Author

Antti Karttunen, May 23 2019

Status

approved