login
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
OFFSET
1,1
LINKS
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Dec 14 2004
EXTENSIONS
More terms from Ray Chandler, Dec 14 2004
STATUS
approved