A318676 - OEIS

%I #12 Jan 24 2024 21:27:36

%S 1,1,1,5,1,7,1,5,10,11,1,11,1,15,16,21,1,16,1,15,22,23,1,35,26,27,10,

%T 19,1,32,1,21,34,35,36,56,1,39,40,55,1,42,1,27,25,47,1,51,50,36,52,31,

%U 1,70,56,75,58,59,1,96,1,63,31,85,66,62,1,39,70,60,1,80,1,75,41,43,78,72,1,71,91,83,1,130,86,87,88,115,1,131,92,51

%N Sum of divisors of n that have an even number of prime factors (counted with multiplicity).

%H Antti Karttunen, <a href="/A318676/b318676.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = Sum_{d|n} [A008836(d) > 0]*d.

%F a(n) = A000203(n) - A318677(n).

%F For all n >= 1, a(n) >= A318674(n).

%F a(n) = Sum_{d|n} d*A065043(d). - _Antti Karttunen_, Jan 24 2024

%t Array[DivisorSum[#, # &, EvenQ@ PrimeOmega@ # &] &, 92] (* _Michael De Vlieger_, Sep 04 2018 *)

%o (PARI) A318676(n) = sumdiv(n,d,(!(bigomega(d)%2))*d);

%Y Cf. A000203, A008836, A065043, A318674, A318677.

%Y Cf. also A038548, A066839.

%K nonn

%O 1,4

%A _Antti Karttunen_, Sep 04 2018