cp's OEIS Frontend

A336852 a(n) = sigma(A003961(n)) - sigma(n).

%I A336852 #17 Jul 03 2023 14:50:52
%S A336852 0,1,2,6,2,12,4,25,18,14,2,50,4,24,24,90,2,85,4,62,40,20,6,180,26,30,
%T A336852 116,100,2,120,6,301,36,26,48,312,4,36,52,230,2,192,4,98,170,48,6,602,
%U A336852 76,135,48,136,6,504,40,360,64,38,2,456,6,56,268,966,60,192,4,134,84,240,2,1045,6,54,218,172,72,264,4,782
%N A336852 a(n) = sigma(A003961(n)) - sigma(n).
%C A336852 Inverse Möbius transform of A336853(n) = (A003961(n) - n).
%H A336852 Antti Karttunen, <a href="/A336852/b336852.txt">Table of n, a(n) for n = 1..16383</a>
%H A336852 Antti Karttunen, <a href="/A336852/a336852.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A336852 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A336852 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A336852 a(n) = Sum_{d|n} (A003961(d)-d).
%F A336852 a(n) = A003973(n) - A000203(n) = A000203(A003961(n)) - A000203(n).
%F A336852 a(n) = A336851(n) + A286385(n).
%o A336852 (PARI)
%o A336852 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A336852 A336852(n) = (sigma(A003961(n)) - sigma(n));
%o A336852 (PARI) A336852(n) = sumdiv(n,d,A003961(d)-d);
%Y A336852 Cf. A000203, A003961, A003973, A286385, A336851, A336853.
%Y A336852 Cf. A001105 (positions of odd terms), A001359 (positions of 2's).
%K A336852 nonn
%O A336852 1,3
%A A336852 _Antti Karttunen_, Aug 05 2020