A069914 - OEIS

%I #13 Aug 20 2021 00:21:31

%S 0,1,2,6,4,15,6,23,16,27,10,64,12,39,42,72,16,98,18,110,60,63,22,213,

%T 48,75,84,156,28,245,30,201,96,99,102,380,36,111,114,357,40,345,42,

%U 248,248,135,46,618,96,278,150,294,52,478,162,501,168,171,58,924,60,183

%N a(n) = Sum_{d|n} (d-1)*sigma(n/d).

%H Ivan Neretin, <a href="/A069914/b069914.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A060640(n) - A007429(n).

%F G.f.: Sum_{k>=1} sigma(k) * x^(2*k) / (1 - x^k)^2. - _Ilya Gutkovskiy_, Aug 19 2021

%t Table[Plus @@ (DivisorSigma[1, ds = Divisors[n]]*(n/ds - 1)), {n, 62}] (* _Ivan Neretin_, May 17 2015 *)

%o (PARI) a(n) = sumdiv(n, d, (d-1)*sigma(n/d)) \\ _Michel Marcus_, Jun 17 2013

%Y Cf. A000203, A006579, A007429, A060640.

%K nonn

%O 1,3

%A _Vladeta Jovovic_, May 04 2002