A353959 - OEIS

A353959

a(n) = Sum_{d|n} d * (-1)^(d'), where d' is the arithmetic derivative of d (A003415).

1, -1, -2, 3, -4, -10, -6, 11, 7, -16, -10, 6, -12, -22, 8, 27, -16, -19, -18, 8, 12, -34, -22, 38, 21, -40, -20, 10, -28, -40, -30, 59, 20, -52, 24, 33, -36, -58, 24, 56, -40, -52, -42, 14, -28, -70, -46, 102, 43, -41, 32, 16, -52, -100, 40, 74, 36, -88, -58, 56, -60, -94

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..62.

MATHEMATICA

d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := DivisorSum[n, # * (-1)^d[#] &]; Array[a, 100] (* Amiram Eldar, May 12 2022 *)

PROG

(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415

a(n) = sumdiv(n, d, d*(-1)^ad(d)); \\ Michel Marcus, May 12 2022

CROSSREFS

Cf. A000005 (tau), A003415 (n').

Sequence in context: A065634 A364223 A087548 * A111619 A241083 A334463

Adjacent sequences: A353956 A353957 A353958 * A353960 A353961 A353962

KEYWORD

sign

AUTHOR

Wesley Ivan Hurt, May 12 2022

STATUS

approved