A240529 Indices of 9-almost prime triangular numbers.

224, 351, 624, 704, 735, 768, 783, 800, 832, 864, 895, 944, 959, 960, 999, 1151, 1152, 1224, 1279, 1343, 1344, 1375, 1440, 1520, 1539, 1824, 1855, 1935, 1943, 1944, 1952, 2000, 2144, 2159, 2176, 2187, 2295, 2367, 2430, 2432, 2464, 2495, 2496, 2499, 2511

Offset

1,1

Links

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

Formula

{ m : A069904(m) = 9 }. - Alois P. Heinz, Aug 05 2019

Example

a(1) = 224 because A000217(224) = 224*(224+1)/2 = 25200 = 2^4 * 3^2 * 5^2 * 7 is a 9-almost prime.

Mathematica

Flatten[Position[Accumulate[Range[3500]], _?(PrimeOmega[#]== 9 &)]]
Select[Range[3000], PrimeOmega[(# (# + 1))/2] == 9 &] (* Harvey P. Dale, Jun 22 2017 *)

Prog

(Magma) [n: n in [2..2600] | &+[d[2]: d in Factorization((n*(n+1)))] eq 10]; // Vincenzo Librandi, Dec 22 2018
(GAP) F:=List([1..2600], n->Length(Factors(n*(n+1)/2)));; a:=Filtered([1..Length(F)], i->F[i]=9); # Muniru A Asiru, Dec 22 2018

Crossrefs

Cf. A000217, A069904, A108815, A114435, A114436, A114437, A164977.

Sequence in context: A345543 A345796 A046296 * A177770 A202442 A331371

Adjacent sequences: A240526 A240527 A240528 * A240530 A240531 A240532

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 07 2014

Status

approved