login
a(n) = A048675(sigma(n)).
7

%I #11 Feb 08 2020 20:44:56

%S 0,2,2,8,3,4,3,6,32,5,4,10,9,5,5,1024,5,34,6,11,5,6,5,8,1024,11,7,11,

%T 7,7,5,12,6,7,6,40,129,8,11,9,11,7,18,12,35,7,6,1026,130,1026,7,17,7,

%U 9,7,9,8,9,8,13,1025,7,35,1073741824,12,8,66,13,7,8,7,38,2049,131,1026,14,7,13,8,1027,32,13,12,13,8,20,9

%N a(n) = A048675(sigma(n)).

%H Antti Karttunen, <a href="/A331750/b331750.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A048675(A000203(n)).

%F Additive with a(p^e) = A048675(sigma(p^e)) = A048675(1 + p + p^2 + ... + p^e).

%t {0}~Join~Array[Total@ Map[#[[-1]]*2^(PrimePi[#[[1]]] - 1) &, FactorInteger@ DivisorSigma[1, #]] &, 86, 2] (* _Michael De Vlieger_, Feb 08 2020, after _Jean-François Alcover_ at A048675 *)

%o (PARI)

%o A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };

%o A331750(n) = A048675(sigma(n));

%Y Cf. A000203, A048675, A324573, A331751.

%K nonn

%O 1,2

%A _Antti Karttunen_, Feb 05 2020