A203173 - OEIS

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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

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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