|
%I #15 Sep 04 2022 01:17:26
%S 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,
%T 30,23,29,56,31,2,14,53,12,29,37,59,16,17,41,74,43,35,53,71,47,11,7,
%U 67,20,41,53,110,16,23,22,89,59,56,61,95,73,2,18,110,67,53,26,108,71,29
%N Sum of the divisors of n whose arithmetic derivative is odd.
%F a(n) = Sum_{d|n} d * ((d') mod 2).
%p A353956 := proc(n)
%p add(d*modp(A003415(d),2), d=numtheory[divisors](n)) ;
%p end proc:
%p seq(A353956(n),n=1..80) ; # _R. J. Mathar_, Jul 05 2022
%t 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 *)
%o (PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
%o a(n) = sumdiv(n, d, if (ad(d) %2, d)); \\ _Michel Marcus_, May 12 2022
%Y Cf. A000005 (tau), A003415 (n'), A353235.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, May 12 2022
|
