

A203173


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


0



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
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OFFSET

1,1


COMMENTS

Central polygonal numbers are those of the form n^2n+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(n1)); 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: A020248 A225705 A259758 * A194532 A065827 A318036
Adjacent sequences: A203170 A203171 A203172 * A203174 A203175 A203176


KEYWORD

nonn


AUTHOR

Franklin T. AdamsWatters, Dec 30 2011


STATUS

approved



