A114437 Indices of 6-almost prime triangular numbers.

32, 48, 96, 99, 104, 111, 119, 120, 125, 152, 161, 168, 176, 188, 189, 195, 200, 208, 223, 231, 239, 240, 252, 260, 264, 275, 299, 300, 303, 304, 315, 336, 342, 343, 344, 352, 359, 363, 374, 377, 391, 392, 395, 400

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Almost Prime.

Eric Weisstein's World of Mathematics, Triangular Number.

Formula

{a(n)} = {k such that A001222(A000217(k)) = 6}. {a(n)} = {k such that k*(k+1)/2 has exactly 6 prime factors, with multiplicity}.

{a(n)} = {k such that A000217(k) is an element of A046306}.

{ m : A069904(m) = 6 }. - Alois P. Heinz, Aug 05 2019

Example

a(1) = 48 because T(48) = TriangularNumber(48) = 48*(48+1)/2 = 1176 = 2^3 * 3 * 7^2 is a 6-almost prime.
a(2) = 96 because T(96) = 96*(96+1)/2 = 4656 = 2^4 * 3 * 97 is a 6-almost prime.
a(18) = 200 because T(200) = 200*(200+1)/2 = 20100 = 2^2 * 3 * 5^2 * 67 is a 6-almost prime.
a(29) = 300 because T(300) = 300*(300+1)/2 = 45150 = 2 * 3 * 5^2 * 7 * 43 is a 6-almost prime.
a(38) = 363 because T(363) = 363*(363+1)/2 = 45150 = 66066 = 2 * 3 * 7 * 11^2 * 13 is a 6-almost prime.

Mathematica

Select[Range[400], PrimeOmega[(#(#+1))/2]==6&] (* Harvey P. Dale, Mar 29 2012 *)
Flatten[Position[Accumulate[Range[800]], _?(PrimeOmega[#]== 6 &)]] (* Vincenzo Librandi, Apr 09 2014 *)

Prog

(PARI) isA114437(n)=bigomega(n*(n+1)/2)==6 /* Michael B. Porter, Mar 30 2012 */

Crossrefs

Cf. A000217, A001222, A046306, A069904.

Sequence in context: A046371 A348824 A175162 * A039379 A043202 A043982

Adjacent sequences: A114434 A114435 A114436 * A114438 A114439 A114440

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 14 2006

Extensions

Corrected by Harvey P. Dale, Mar 29 2012

Status

approved