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 A378231 #10 Nov 23 2024 19:37:34
%S A378231 1,5,19,41,41,47,109,365,469,141,155,299,271,449,683,3281,341,1097,
%T A378231 505,1041,1927,663,811,2567,2001,1211,11719,3509,929,-921,1331,29525,
%U A378231 2777,1545,4277,6749,1639,2333,4933,9141,1805,851,2161,5235,16733,3815,2755,22979,13177,6805,6239,9671,3421,27347,6131,31049
%N A378231 Deficiency of prime-shifted squares: a(n) = 2*A003961(n^2) - sigma(A003961(n^2)), where A003961 is fully multiplicative function with a(prime(i)) = prime(i+1).
%C A378231 See comments in A377879 and in A337339.
%H A378231 Antti Karttunen, <a href="/A378231/b378231.txt">Table of n, a(n) for n = 1..20000</a>
%H A378231 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%H A378231 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A378231 a(n) = A344587(n^2) = A377879(A003961(n)).
%o A378231 (PARI)
%o A378231 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A378231 A344587(n) = { my(u=A003961(n)); (u+u - sigma(u)); };
%o A378231 A378231(n) = A344587(n^2);
%Y A378231 Cf. A000203, A003961, A003973, A033879, A344587, A377879.
%Y A378231 Cf. also A337339.
%K A378231 sign
%O A378231 1,2
%A A378231 _Antti Karttunen_, Nov 23 2024