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%I #24 Sep 08 2022 08:45:16
%S 255,384,511,575,639,728,767,896,1088,1295,1376,1407,1599,1700,1727,
%T 1792,1919,1920,2015,2024,2375,2431,2672,2815,2880,2915,2944,2975,
%U 3104,3159,3199,3327,3375,3392,3456,3583,3744,3999,4031,4032,4160,4223,4256
%N Indices of triangular numbers which are 10-almost primes. Indices of A101744.
%H Muniru A Asiru, <a href="/A101745/b101745.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n)*(a(n)+1)/2 has exactly 10 prime factors.
%F { m : A069904(m) = 10 }. - _Alois P. Heinz_, Aug 05 2019
%e 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.
%t 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 *)
%t Flatten[Position[Accumulate[Range[5000]],_?(PrimeOmega[#]==10&)]] (* _Harvey P. Dale_, May 12 2011 *)
%o (Magma) [n: n in [2..4500] | &+[d[2]: d in Factorization((n*(n+1)))] eq 11]; // _Vincenzo Librandi_, Dec 22 2018
%o (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
%Y Cf. A101744, A000217, A046314, A076550, A069904.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Dec 14 2004
%E More terms from _Ray Chandler_, Dec 14 2004
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