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

Author

Vincenzo Librandi, Apr 07 2014

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

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

Programs

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

Magma

[n: n in [2..2600] | &+[d[2]: d in Factorization((n*(n+1)))] eq 10]; // Vincenzo Librandi, Dec 22 2018

Mathematica

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

Formula

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