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

1,1

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.

Links

Table of n, a(n) for n=1..39.

Example

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

Prog

(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", ")))

Crossrefs

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

Sequence in context: A225705 A259758 A353056 * A194532 A065827 A318036

Adjacent sequences: A203170 A203171 A203172 * A203174 A203175 A203176

Keyword

nonn

Author

Franklin T. Adams-Watters, Dec 30 2011

Status

approved