

A253651


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


4



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
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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 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


AUTHOR

Antonio Roldán, Jan 07 2015


STATUS

approved



