A342926 a(n) = A003415(sigma(n)) - n, where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.

-1, -1, 1, -3, 0, 10, 5, 0, -8, 11, 5, 20, -4, 30, 29, -15, 4, -2, 5, 21, 59, 38, 21, 68, -24, 15, 41, 64, 2, 126, 49, 19, 79, 47, 77, -16, -16, 54, 53, 83, 0, 230, 5, 80, 26, 110, 65, 80, -27, -16, 105, 25, 28, 190, 101, 188, 119, 65, 33, 272, -28, 210, 101, -63, 59, 318, 5, 97, 203, 314, 85, 47, -34, 27, 53, 112, 195

Offset: 1

Author

Antti Karttunen, Apr 08 2021

Keywords

• sign

Links

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

Crossrefs

Cf. A342925, A342924, A343223 [= gcd(A003415(n), a(n))].

Cf. A342021 (positions of 0's), A343216 (of negative terms), A343217 (of nonnegative terms), A343218 (of positive terms).

Programs

Mathematica

Array[If[#2 < 2, 0, #2 Total[#2/#1 & @@@ FactorInteger[#2]]] - #1 & @@ {#, DivisorSigma[1, #]} &, 77] (* Michael De Vlieger, Apr 08 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342926(n) = (A003415(sigma(n))-n);

Formula

a(n) = A342925(n) - n = A003415(A000203(n)) - n.