This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378752 #7 Dec 09 2024 19:45:35
%S A378752 1,2,2,1,4,0,4,-10,-5,4,10,-22,10,0,0,-59,16,-46,16,-20,-8,16,18,-120,
%T A378752 5,12,-76,-44,28,-48,26,-238,12,28,0,-221,34,24,4,-140,40,-96,40,-14,
%U A378752 -92,24,42,-478,-19,-42,24,-38,48,-384,32,-240,16,52,58,-288,56,40,-164,-839,24,-48,64,-8,12,-96,70,-850,68,60
%N A378752 a(n) = 2*sigma(n) - sigma(A003961(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).
%H A378752 Antti Karttunen, <a href="/A378752/b378752.txt">Table of n, a(n) for n = 1..20000</a>
%H A378752 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>
%H A378752 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A378752 a(n) = 2*A000203(n) - A003973(n).
%o A378752 (PARI)
%o A378752 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A378752 A378752(n) = ((2*sigma(n)) - sigma(A003961(n)));
%Y A378752 Cf A000203, A003961, A003973.
%Y A378752 Cf. A337381 (positions of terms <= 0), A337382 (of terms > 0), A337384 (positions of 0's),
%K A378752 sign
%O A378752 1,2
%A A378752 _Antti Karttunen_, Dec 09 2024