A114436 Indices of 5-almost prime triangular numbers.

15, 24, 27, 31, 35, 39, 44, 47, 54, 55, 56, 71, 72, 75, 79, 81, 84, 87, 90, 98, 107, 108, 112, 116, 124, 132, 134, 140, 147, 153, 155, 162, 164, 167, 170, 171, 174, 179, 180, 183, 184, 199, 203, 204, 209, 219, 220, 225, 230, 234, 244, 245, 247, 248, 249

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Eric Weisstein's World of Mathematics, Triangular Number.

Eric Weisstein's World of Mathematics, Almost Prime.

Formula

{a(n)} = {k such that A001222(A000217(k)) = 5}. {a(n)} = {k such that k*(k+1)/2 has exactly 5 prime factors, with multiplicity}. {a(n)} = {k such that A000217(k) is an element of A014614}.

{ m : A069904(m) = 5 }. - Alois P. Heinz, Aug 05 2019

Example

a(1) = 15 because T(15) = TriangularNumber(15) = 15*(15+1)/2 = 120 = 2^3 * 3 * 5 is a 5-almost prime.
a(2) = 24 because T(24) = 24*(24+1)/2 = 300 = 2^2 * 3 * 5^2 is a 5-almost prime.
a(3) = 27 because T(27) = 27*(27+1)/2 = 378 = 2 * 3^3 * 7 is a 5-almost prime.
a(4) = 31 because T(27) = 31*(31+1)/2 = 496 = 2^4 * 31 is a 5-almost prime.
a(17) = 84 because T(27) = 84*(84+1)/2 = 3570 = 2 * 3 * 5 * 7 * 17 is a 5-almost prime.

Mathematica

Select[Range[250], PrimeOmega[(#(#+1))/2]==5&] (* Harvey P. Dale, Sep 14 2012 *)
Flatten[Position[Accumulate[Range[700]], _?(PrimeOmega[#]== 5 &)]] (* Vincenzo Librandi, Apr 09 2014 *)

Crossrefs

Cf. A000217, A001222, A014614, A069904.

Sequence in context: A059144 A274339 A343053 * A114558 A035408 A173035

Adjacent sequences: A114433 A114434 A114435 * A114437 A114438 A114439

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 13 2006

Extensions

Corrected and extended by Harvey P. Dale, Apr 02 2011

Status

approved