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%I #16 May 22 2021 09:05:14
%S 0,1,4,8,11,12,17,25,26,27,28,29,37,38,41,45,48,54,60,67,71,73,75,77,
%T 88,92,94,114,115,116,119,133
%N Integers k such that k! + 1 is the sum of 2 nonzero squares.
%e a(3) = 4 because 4! + 1 = 4^2 + 3^2.
%t Flatten@ Position[Map[Length, Map[Map[Length, PowersRepresentations[#, 2, 2] &@(#! + 1) /. 0 -> Nothing] &, Range[0, 48]] /. 1 -> Nothing], n_ /; n > 0] - 1 (* _Michael De Vlieger_, Nov 28 2015 *)
%o (PARI) is(n) = { for(i=1, #n=factor(n!+1)~%4, n[1, i]==3 && n[2, i]%2 && return); n && (vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)) }
%Y Cf. A000404, A038507, A264665, A271186.
%K nonn,more
%O 1,3
%A _Altug Alkan_, Nov 27 2015
%E a(25)-a(32) from _Jinyuan Wang_, May 22 2021