A253652 Triangular numbers that are the product of a triangular number and an oblong number.

0, 6, 36, 120, 210, 300, 630, 1176, 2016, 3240, 3570, 4950, 7140, 7260, 10296, 14196, 19110, 23436, 25200, 32640, 39060, 41616, 52326, 61776, 64980, 79800, 97020, 116886, 139656, 145530, 165600, 195000, 228150, 242556, 265356, 304590, 306936, 349866, 353220, 404550, 426426, 461280

Offset

1,2

Comments

Supersequence of A083374, because A083374(n)= n^2 * (n^2 - 1)/2 = n*(n+1)/2*n*(n-1), product of triangular number n*(n+1)/2 and oblong number n*(n-1).

Links

Table of n, a(n) for n=1..42.

Example

630 is in the sequence because it is a triangular number (630 = 35*36/2) and 630 = 105*6, with 105 = 14*15/2, triangular number, and 6 = 2*3, oblong number.

Prog

(PARI) {i=0; j=1; print1(0, ", "); while(i<=10^6, k=1; p=2; c=0; while(k<i&&c==0, if(i/k==i\k&&issquare(4*(i/k)+1)&&k>0, c=k); if(c>0, print1(i, ", ")); k+=p; p+=1); i+=j; j+=1)}

Crossrefs

Cf. A002378, A000217, A188630, A083374, A253650, A253651, A253653.

Sequence in context: A207718 A262467 A225262 * A375608 A083374 A264366

Adjacent sequences: A253649 A253650 A253651 * A253653 A253654 A253655

Keyword

nonn

Author

Antonio Roldán, Jan 07 2015

Status

approved