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

1,1

Links

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

Formula

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

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A359445 A306223 A023690 * A182221 A053339 A031197

Adjacent sequences: A101742 A101743 A101744 * A101746 A101747 A101748

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 14 2004

Extensions

More terms from Ray Chandler, Dec 14 2004

Status

approved