A253651 Triangular numbers that are the product of a triangular number and a prime number.

0, 3, 6, 15, 21, 45, 66, 78, 105, 190, 210, 231, 435, 465, 630, 861, 903, 1035, 1326, 2415, 2556, 2628, 3003, 3570, 4005, 4950, 5460, 5565, 5995, 7140, 8646, 8778, 9870, 12246, 16471, 16836, 17205, 17391, 17766, 20100, 22155, 26565, 26796, 28680, 28920, 30381, 32131, 33411, 33930, 36856

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..259 (all terms up to and including the 10000th triangular number)

Example

190 is in the sequence because it is triangular (190=19*20/2) and 190=10*19, with 10 triangular number and 19 prime number.

Maple

N:= 10^5: # to get all terms <= N
Primes:= select(isprime, [2, seq(2*k+1, k=1..N/3)]):
select(t -> issqr(1+8*t), {seq(seq(a*(a+1)/2*p, a = 2 .. floor(sqrt(2*N/p))), p = Primes)});
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%, list)); # Robert Israel, Jan 07 2015

Mathematica

Join[{0}, Module[{nn=300, trs}, trs=Accumulate[Range[nn]]; Select[ trs, AnyTrue[ #/trs, PrimeQ]&]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 16 2018 *)

Prog

(PARI) {i=1; j=2; print1(0, ", "); while(i<=10^5, k=1; p=2; c=0; while(k<i&&c==0, if(i/k==i\k&&isprime(i/k)&&i/k>1, c=k); if(c>0, print1(i, ", ")); k+=p; p+=1); i+=j; j+=1)}

Crossrefs

Cf. A029549 (T is 2*t), A076140 (T is 3*t), A225503 (first T to be prime(n)*t).

Cf. A188630, A253650, A253652, A253653.

Sequence in context: A061066 A093799 A087359 * A180322 A244164 A129602

Adjacent sequences: A253648 A253649 A253650 * A253652 A253653 A253654

Keyword

nonn,changed

Author

Antonio Roldán, Jan 07 2015

Status

approved