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 A377986 #12 Nov 21 2024 15:30:21
%S A377986 0,0,0,1,1,1,2,1,2,6,0,4,4,3,7
%N A377986 Number of integers k, with bigomega(k) > 2, whose arithmetic derivative (A003415) is equal to n!, the n-th factorial.
%C A377986 The solutions (composite, nonsemiprime antiderivatives of n!) are given in A377987.
%H A377986 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A377986 a(n) = Sum_{k=1..A002620(n!)} [A003415(k) = n! and A001222(k) > 2], where [ ] is the Iverson bracket.
%F A377986 a(n) = A376410(n) - A062311(n).
%e A377986 See the examples in A377987.
%o A377986 (PARI)
%o A377986 A002620(n) = ((n^2)>>2);
%o A377986 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A377986 A377986(n) = { my(g=n!); sum(k=1,A002620(g),(bigomega(k)>2) && (A003415(k)==g)); };
%o A377986 (PARI) A377986(n) = AntiDeriv(n!,2,"a_terms_for_A377987_unsorted.txt"); \\ The rest of the program is given in A376410.
%Y A377986 Row lengths of irregular triangle A377987.
%Y A377986 Cf. A000142, A002620, A003415, A062311, A376410.
%K A377986 nonn,hard,more
%O A377986 1,7
%A A377986 _Antti Karttunen_, Nov 19 2024