OFFSET
1,1
COMMENTS
A101745 contains the indices of this sequence, i.e. T(n) for what values of n are these 10-almost primes.
REFERENCES
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 59, 1987.
Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 33-38, 1996.
Dudeney, H. E. Amusements in Mathematics. New York: Dover, pp. 67 and 167, 1970.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Triangular Number.
Eric Weisstein's World of Mathematics, Almost Prime.
FORMULA
EXAMPLE
a(1) = 32640 because that is the smallest 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]]]; Select[Table[n*(n+1)/2, {n, 2, 5000}], BigOmega[ # ]==10&] (* Ray Chandler, Dec 14 2004 *)
PROG
(PARI) list(lim)=my(v=List(), cur, last=3, n=256, t); while((t=n*(n-1)/2) <= lim, cur=bigomega(n); if(cur+old==11, listput(v, t)); old=cur; n++); Vec(v) \\ Charles R Greathouse IV, Feb 05 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Dec 14 2004
EXTENSIONS
More terms from Ray Chandler, Dec 14 2004
STATUS
approved