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A253652 Triangular numbers that are the product of a triangular number and an oblong number. 3

%I

%S 0,6,36,120,210,300,630,1176,2016,3240,3570,4950,7140,7260,10296,

%T 14196,19110,23436,25200,32640,39060,41616,52326,61776,64980,79800,

%U 97020,116886,139656,145530,165600,195000,228150,242556,265356,304590,306936,349866,353220,404550,426426,461280

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

%C 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).

%e 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.

%o (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)}

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

%K nonn

%O 1,2

%A _Antonio Roldán_, Jan 07 2015

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Last modified September 17 12:56 EDT 2019. Contains 327131 sequences. (Running on oeis4.)