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A353958
Sum of the divisors of n whose arithmetic derivative is even.
0
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 12 2022
STATUS
approved