A353958 Sum of the divisors of n whose arithmetic derivative is even.

1, 1, 1, 5, 1, 1, 1, 13, 10, 1, 1, 17, 1, 1, 16, 29, 1, 10, 1, 25, 22, 1, 1, 49, 26, 1, 10, 33, 1, 16, 1, 61, 34, 1, 36, 62, 1, 1, 40, 73, 1, 22, 1, 49, 25, 1, 1, 113, 50, 26, 52, 57, 1, 10, 56, 97, 58, 1, 1, 112, 1, 1, 31, 125, 66, 34, 1, 73, 70, 36, 1, 166, 1, 1, 41, 81, 78

Offset

1,4

Links

Table of n, a(n) for n=1..77.

Formula

a(n) = Sum_{d|n} d * ((1+d') mod 2).

Mathematica

d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := DivisorSum[n, # &, EvenQ[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, if (!(ad(d) % 2), d)); \\ Michel Marcus, May 12 2022

Crossrefs

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

Sequence in context: A360722 A091051 A183097 * A285486 A230368 A256690

Adjacent sequences: A353955 A353956 A353957 * A353959 A353960 A353961

Keyword

nonn

Author

Wesley Ivan Hurt, May 12 2022

Status

approved