A101745 Indices of triangular numbers which are 10-almost primes. Indices of A101744.

255, 384, 511, 575, 639, 728, 767, 896, 1088, 1295, 1376, 1407, 1599, 1700, 1727, 1792, 1919, 1920, 2015, 2024, 2375, 2431, 2672, 2815, 2880, 2915, 2944, 2975, 3104, 3159, 3199, 3327, 3375, 3392, 3456, 3583, 3744, 3999, 4031, 4032, 4160, 4223, 4256

Offset: 1

Author

Jonathan Vos Post, Dec 14 2004

Keywords

• easy
• nonn

Examples

			a(1) = 255 because that is the smallest index of a triangular number which is also a 10-almost prime; specifically T(255) = 255*(255+1)/2 = 32640 = 2^7 * 3 * 5 * 17.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A101744, A000217, A046314, A076550, A069904.

Programs

GAP

F:=List([1..4300],n->Length(Factors(n*(n+1)/2)));; a:=Filtered([1..Length(F)],i->F[i]=10); # Muniru A Asiru, Dec 22 2018

Magma

[n: n in [2..4500] | &+[d[2]: d in Factorization((n*(n+1)))] eq 11]; // Vincenzo Librandi, Dec 22 2018

Mathematica

BigOmega[n_Integer]:=Plus@@Last[Transpose[FactorInteger[n]]]; Do[ t=n*(n+1)/2; If[BigOmega[t]==10, Print[n, " ", t];];, {n, 2, 5000}]; (* Ray Chandler, Dec 14 2004 *)
Flatten[Position[Accumulate[Range[5000]],?(PrimeOmega[#]==10&)]] (* _Harvey P. Dale, May 12 2011 *)

Formula

a(n)*(a(n)+1)/2 has exactly 10 prime factors.

{ m : A069904(m) = 10 }. - Alois P. Heinz, Aug 05 2019

Extensions

More terms from Ray Chandler, Dec 14 2004