A353961 a(n) = Sum_{d|n} d' * (-1)^(d'), where d' is the arithmetic derivative of d (A003415).

0, -1, -1, 3, -1, -7, -1, 15, 5, -9, -1, 13, -1, -11, 6, 47, -1, -22, -1, 19, 8, -15, -1, 69, 9, -17, -22, 25, -1, -38, -1, 127, 12, -21, 10, 58, -1, -23, 14, 99, -1, -48, -1, 37, -27, -27, -1, 213, 13, -44, 18, 43, -1, -130, 14, 129, 20, -33, -1, 98, -1, -35, -37, 319, 16, -68

Offset

1,4

Links

Table of n, a(n) for n=1..66.

Mathematica

d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := DivisorSum[n, d[#] * (-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, my(dd=ad(d)); dd*(-1)^dd); \\ Michel Marcus, May 13 2022

Crossrefs

Cf. A003415 (n').

Sequence in context: A094024 A297172 A329034 * A290678 A290422 A352402

Adjacent sequences: A353958 A353959 A353960 * A353962 A353963 A353964

Keyword

sign

Author

Wesley Ivan Hurt, May 12 2022

Status

approved