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%I #12 Mar 07 2016 12:55:44
%S 2,12,24,25,26,48,50,60,73,74,96,97,120,121,122,145,146,156,169,194,
%T 204,240,242,289,312,337,338,348,361,362,410,432,457,480,492,529,554,
%U 578,600,624,673,722,732,768,793,842,865,866,876,960,961,985
%N Integers n such that A000330(n) is the sum of 2 nonzero squares.
%C Corresponding square pyramidal numbers are 5, 650, 4900, 5525, 6201, 38024, 42925, 73810, 132349, 137825, 299536, 308945, 583220, 597861, 612745, 1026745, ...
%e 12 is a term because A000330(12) = 1^2 + 2^2 + ... + 11^2 + 12^2 = 650 = 5^2 + 25^2.
%t Select[Range@ 1000, SquaresR[2, Binomial[# + 2, 3] + Binomial[# + 1, 3]] > 0 &] (* _Michael De Vlieger_, Mar 06 2016 *)
%o (PARI) isA000404(n) = {for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)); }
%o for(n=0, 1e3, if(isA000404(n*(n+1)*(2*n+1)/6), print1(n, ", ")));
%Y Cf. A000330, A000404.
%K nonn
%O 1,1
%A _Altug Alkan_, Mar 06 2016