cp's OEIS Frontend

A203173 Central polygonal numbers that are nontrivially the product of two central polygonal numbers.

%I A203173 #8 Dec 10 2016 19:25:21
%S A203173 21,91,273,651,931,1333,2451,3783,4161,4557,6643,10101,14763,20881,
%T A203173 22351,28731,31863,38613,50851,52671,65793,83811,99541,105301,130683,
%U A203173 139503,160401,194923,221371,234741,235711,280371,316407,332353,391251,427063,457653,532171,615441
%N A203173 Central polygonal numbers that are nontrivially the product of two central polygonal numbers.
%C A203173 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 A203173 21 = 4^2+4+1 = 7*3 = (2^2+2+1)*(1^2+1+1), so 21 is in the sequence.
%o A203173 (PARI) iscpn(n)=local(r=sqrtint(n-1));n==r^2+r+1
%o A203173 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 A203173 ap(n)=for(k=1,n,if(iscpnprod(k^2+k+1),print1(k^2+k+1", ")))
%Y A203173 Cf. A002061 (central polygonal numbers), A059826 (a subsequence except for first two terms).
%K A203173 nonn
%O A203173 1,1
%A A203173 _Franklin T. Adams-Watters_, Dec 30 2011