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 A374671 #9 Jul 18 2024 14:27:28
%S A374671 8,19,23,44,45,57,67,76,80,83,84,85,105,107,116,120,123,140,141,146,
%T A374671 158,161,165,174,177,187,201,208,214,225,235,239,241,243,244,246,247,
%U A374671 263,269,272,277,284,297,309,315,321,322,325,337,339,341,342,344,360,363
%N A374671 Positive numbers k such that k! and (k+1)! have an equal number of infinitary divisors.
%C A374671 Positive numbers such that k! and (k+1)! have an equal number of Fermi-Dirac factors (A064547).
%C A374671 Positive numbers k such that A037445(k!) = A037445((k+1)!).
%C A374671 Positive numbers k such that A064547(k!) = A064547((k+1)!).
%C A374671 Positive numbers k such that A177329(k) = A177329(k+1).
%H A374671 Amiram Eldar, <a href="/A374671/b374671.txt">Table of n, a(n) for n = 1..10000</a>
%e A374671 8 is a term since A037445(8!) = A037445(9!) = 64.
%t A374671 s[n_] := s[n] = Module[{e = FactorInteger[n!][[;; , 2]]}, Sum[DigitCount[e[[k]], 2, 1], {k, 1, Length[e]}]]; Select[Range[2, 400], s[#] == s[# + 1] &]
%o A374671 (PARI) s(n) = {my(e = factor(n!)[, 2]); sum(k=1, #e, hammingweight(e[k]));}
%o A374671 lista(kmax) = {my(s1 = s(1), s2); for(k = 2, kmax, s2 = s(k); if(s1 == s2, print1(k-1, ", ")); s1 = s2);}
%Y A374671 Cf. A037445, A064547, A177329, A343819, A374672, A374673, A374674.
%K A374671 nonn
%O A374671 1,1
%A A374671 _Amiram Eldar_, Jul 16 2024