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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 16 00:33 EST 2019. Contains 330013 sequences. (Running on oeis4.)