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A114436 Indices of 5-almost prime triangular numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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}.

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.

Sequence in context: A166657 A059144 A274339 * 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

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Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)