A353956 Sum of the divisors of n whose arithmetic derivative is odd.

0, 2, 3, 2, 5, 11, 7, 2, 3, 17, 11, 11, 13, 23, 8, 2, 17, 29, 19, 17, 10, 35, 23, 11, 5, 41, 30, 23, 29, 56, 31, 2, 14, 53, 12, 29, 37, 59, 16, 17, 41, 74, 43, 35, 53, 71, 47, 11, 7, 67, 20, 41, 53, 110, 16, 23, 22, 89, 59, 56, 61, 95, 73, 2, 18, 110, 67, 53, 26, 108, 71, 29

Offset

1,2

Links

Table of n, a(n) for n=1..72.

Formula

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

Maple

A353956 := proc(n)
    add(d*modp(A003415(d), 2), d=numtheory[divisors](n)) ;
end proc:
seq(A353956(n), n=1..80) ; # R. J. Mathar, Jul 05 2022

Mathematica

d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := DivisorSum[n, # &, OddQ[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'), A353235.

Sequence in context: A371395 A059098 A082050 * A367633 A183098 A183101

Adjacent sequences: A353953 A353954 A353955 * A353957 A353958 A353959

Keyword

nonn

Author

Wesley Ivan Hurt, May 12 2022

Status

approved