A318505 - OEIS

%I #12 Dec 21 2024 11:10:04

%S 0,0,0,1,0,3,0,3,1,3,0,10,0,3,4,7,0,12,0,12,4,3,0,24,1,3,4,14,0,27,0,

%T 15,4,3,6,37,0,3,4,30,0,33,0,18,18,3,0,52,1,18,4,20,0,39,6,36,4,3,0,

%U 78,0,3,20,31,6,45,0,24,4,39,0,87,0,3,24,26,8,51,0,66,13,3,0,98,6,3,4,48,0,99,8,30,4,3,6,108,0,24,24,67,0,63,0,54,52

%N Sum of divisors of n, up to, but not including the second largest of them A032742(n); a(1) = 0 by convention.

%H Antti Karttunen, <a href="/A318505/b318505.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.

%F a(1) = 0; for n > 1, a(n) = A001065(n) - A032742(n).

%F Sum_{k=1..n} a(k) ~ (zeta(2)/2 - 1/2 - c) * n^2, where c is defined in the corresponding formula in A032742. - _Amiram Eldar_, Dec 21 2024

%o (PARI)

%o A001065(n) = (sigma(n)-n);

%o A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));

%o A318505(n) = if(1==n,0,A001065(n)-A032742(n));

%o A318505(n) = sumdiv(n,d,(d<A032742(n))*d); \\ Alternatively.

%Y Cf. A001065, A013661, A032742, A318504, A318506, A318507, A318508.

%K nonn

%O 1,6

%A _Antti Karttunen_, Aug 27 2018