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%I #8 Dec 10 2016 19:25:21
%S 21,91,273,651,931,1333,2451,3783,4161,4557,6643,10101,14763,20881,
%T 22351,28731,31863,38613,50851,52671,65793,83811,99541,105301,130683,
%U 139503,160401,194923,221371,234741,235711,280371,316407,332353,391251,427063,457653,532171,615441
%N Central polygonal numbers that are nontrivially the product of two central polygonal numbers.
%C Central polygonal numbers are those of the form n^2-n+1, or equivalently n^2+n+1. We exclude factorizations where one of the factors is 1.
%e 21 = 4^2+4+1 = 7*3 = (2^2+2+1)*(1^2+1+1), so 21 is in the sequence.
%o (PARI) iscpn(n)=local(r=sqrtint(n-1));n==r^2+r+1
%o iscpnprod(n)=local(x,y);for(i=1,n,x=i^2+i+1;y=n\x;if(x>y,return(0));if(n==x*y&&iscpn(y),return(1)));0
%o ap(n)=for(k=1,n,if(iscpnprod(k^2+k+1),print1(k^2+k+1", ")))
%Y Cf. A002061 (central polygonal numbers), A059826 (a subsequence except for first two terms).
%K nonn
%O 1,1
%A _Franklin T. Adams-Watters_, Dec 30 2011
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