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A101745 Indices of triangular numbers which are 10-almost primes. Indices of A101744. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A257021 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

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Last modified September 16 05:49 EDT 2021. Contains 347469 sequences. (Running on oeis4.)