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 A344587 #24 Nov 23 2024 19:37:29
%S A344587 1,2,4,5,6,6,10,14,19,10,12,12,16,18,22,41,18,26,22,22,38,22,28,30,41,
%T A344587 30,94,42,30,18,36,122,46,34,58,47,40,42,62,58,42,42,46,52,102,54,52,
%U A344587 84,109,66,70,72,58,126,70,114,86,58,60,6,66,70,178,365,94,54,70,82,110,78,72,110,78,78,148,102,118,78
%N A344587 Deficiency of prime-shifted n: a(n) = 2*A003961(n) - sigma(A003961(n)).
%C A344587 First negative value occurs as a(120) = -30.
%C A344587 Questions: Which subsets of natural numbers generate the "cut sigmoid" graph(s) that cross the X-axis in the (lowermost) scatter plot?
%H A344587 Antti Karttunen, <a href="/A344587/b344587.txt">Table of n, a(n) for n = 1..65537</a>
%H A344587 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A344587 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A344587 a(n) = A033879(A003961(n)) = 2*A003961(n) - A003973(n).
%F A344587 a(n) = Sum_{d|n} A337544(d).
%F A344587 From _Antti Karttunen_, Nov 23 2024: (Start)
%F A344587 a(n) = Sum_{d|n} A003961(d)*A153881(n/d) = A003961(n) - A336851(n).
%F A344587 a(n) = Sum_{d|n} A033879(d)*A349387(n/d).
%F A344587 a(n) = Sum_{d|n} A003972(d)*A378216(n/d).
%F A344587 (End)
%o A344587 (PARI)
%o A344587 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A344587 A344587(n) = { my(u=A003961(n)); (u+u - sigma(u)); };
%Y A344587 Cf. A000203, A003961, A003973, A033879, A153881, A336851, A337386 (positions of terms <= 0), A346246 (Dirichlet inverse), A349387, A378216, A378231 [= a(n^2)].
%Y A344587 Inverse Möbius transform of A337544.
%K A344587 sign,look
%O A344587 1,2
%A A344587 _Antti Karttunen_, May 28 2021