

A114436


Indices of 5almost prime triangular numbers.


5



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



