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A253650 Triangular numbers that are the product of a triangular number and a square number (both greater than 1). 4
300, 1176, 3240, 7260, 14196, 25200, 29403, 41616, 64980, 97020, 139656, 195000, 228150, 265356, 353220, 461280, 592416, 749700, 936396, 1043290, 1155960, 1412040, 1708476, 2049300, 2438736, 2881200, 3381300, 3499335, 3943836, 4573800, 5276376, 6056940, 6921060, 7874496 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..3486

EXAMPLE

3240 is in the sequence because 3240 is triangular number (3240=80*81/2), and 3240=10*324=(4*5/2)*(18^2), product of triangular number 10 and square number 324.

MATHEMATICA

triQ[n_] := IntegerQ@ Sqrt[8n + 1]; lst = Sort@ Flatten@ Outer[Times, Table[ n(n + 1)/2, {n, 2, 400}], Table[ n^2, {n, 2, 200}]]; Select[ lst, triQ] (* Robert G. Wilson v, Jan 13 2015 *)

PROG

(PARI) {i=3; j=3; while(i<=10^7, k=3; p=3; c=0; while(k<i&&c==0, if(i/k==i\k&&issquare(i/k)&&i/k>1, c=k); if(c>0, print1(i, ", ")); k+=p; p+=1); i+=j; j+=1)}

(PARI) is(n)=if(!ispolygonal(n, 3), return(0)); fordiv(core(n, 1)[2], d, d>1 && ispolygonal(n/d^2, 3) && n>d^2 && return(1)); 0 \\ Charles R Greathouse IV, Sep 29 2015

(PARI) list(lim)=my(v=List(), t, c); for(n=24, (sqrt(8*lim+1)-1)\2, t=n*(n+1)/2; c=core(n, 1)[2]*core(n+1, 1)[2]; if(valuation(t, 2)\2 < valuation(c, 2), c/=2); fordiv(c, d, if(d>1 && ispolygonal(t/d^2, 3) && t>d^2, listput(v, t); break))); Vec(v) \\ Charles R Greathouse IV, Sep 29 2015

CROSSREFS

Cf. A188630, A083374, A185096, A253651, A253652, A253653.

Sequence in context: A250008 A190879 A154061 * A054026 A237773 A188252

Adjacent sequences:  A253647 A253648 A253649 * A253651 A253652 A253653

KEYWORD

nonn

AUTHOR

Antonio Roldán, Jan 07 2015

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.