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

21, 91, 273, 651, 931, 1333, 2451, 3783, 4161, 4557, 6643, 10101, 14763, 20881, 22351, 28731, 31863, 38613, 50851, 52671, 65793, 83811, 99541, 105301, 130683, 139503, 160401, 194923, 221371, 234741, 235711, 280371, 316407, 332353, 391251, 427063, 457653, 532171, 615441

Offset: 1

Author

Franklin T. Adams-Watters, Dec 30 2011

Keywords

• nonn

Comments

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.

Examples

			21 = 4^2+4+1 = 7*3 = (2^2+2+1)*(1^2+1+1), so 21 is in the sequence.
		

Crossrefs

Cf. A002061 (central polygonal numbers), A059826 (a subsequence except for first two terms).

Programs

PARI

iscpn(n)=local(r=sqrtint(n-1));n==r^2+r+1
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
ap(n)=for(k=1,n,if(iscpnprod(k^2+k+1),print1(k^2+k+1", ")))