

A114437


Indices of 6almost prime triangular numbers.


5



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
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OFFSET

1,1


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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)) = 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 6almost prime.
a(2) = 96 because T(96) = 96*(96+1)/2 = 4656 = 2^4 * 3 * 97 is a 6almost prime.
a(18) = 200 because T(200) = 200*(200+1)/2 = 20100 = 2^2 * 3 * 5^2 * 67 is a 6almost prime.
a(29) = 300 because T(300) = 300*(300+1)/2 = 45150 = 2 * 3 * 5^2 * 7 * 43 is a 6almost prime.
a(38) = 363 because T(363) = 363*(363+1)/2 = 45150 = 66066 = 2 * 3 * 7 * 11^2 * 13 is a 6almost prime (363 and 66066 are both palindromatic).


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: A014614 A046371 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



