A240528 Indices of 8-almost prime triangular numbers.

63, 80, 128, 256, 287, 288, 319, 320, 324, 383, 399, 440, 447, 480, 495, 539, 560, 567, 576, 608, 640, 648, 671, 675, 703, 720, 729, 799, 831, 863, 927, 935, 972, 975, 1000, 1007, 1055, 1056, 1071, 1079, 1080, 1104, 1119, 1120, 1160, 1175, 1183, 1184

Offset: 1

Author

Vincenzo Librandi, Apr 07 2014

Keywords

• nonn

Examples

			a(1) = 63 because A000217(63) = 63*(63+1)/2 = 2016 = 2^5 * 3^2 * 7 is an 8-almost prime.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Crossrefs

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

Cf. A046310 (8-almost primes).

Programs

GAP

F:=List([1..1200],n->Length(Factors(n*(n+1)/2)));; a:=Filtered([1..Length(F)],i->F[i]=8); # Muniru A Asiru, Dec 22 2018

Magma

[n: n in [2..1200] | &+[d[2]: d in Factorization((n*(n+1)))] eq 9]; // Vincenzo Librandi, Dec 22 2018

Mathematica

Flatten[Position[Accumulate[Range[1500]], _?(PrimeOmega[#]== 8 &)]]

Formula

{ m : A069904(m) = 8 }. - Alois P. Heinz, Aug 05 2019