OFFSET
1,4
COMMENTS
We must include multiplicity in the definition due to terms such as a(16) = 29889983 = 19 * 31^2 * 1637. The primes are those n for which a(n) = Omega(A027612(n))= 1, namely a(2) = 5, a(3) = 13, a(6) = 223, a(9) = 4861, a(18) = 197698279, a(25) = 25472027467. The semiprimes are those for which a(n) = 2, such as when n = 4, 5, 7, 8, 11, 12, 13, 15, 19, 23, 24. The 3-almost primes are those for which a(n) = 3, as with the "3-brilliant" a(10) = 55991 = 13 * 59 * 73, a(14), a(17), a(21), a(22), a(26).
REFERENCES
J. H. Conway and R. K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996, pp. 143 and 258-259.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..150
Eric Weisstein's World of Mathematics, Harmonic Number, MathWorld, see discussion of Conway and Guy (1996) definition of the second-order harmonic number.
EXAMPLE
a(20) = 5 because A027612(20) = 41054655 = 3 * 5 * 23 * 127 * 937 has 5 prime factors.
MATHEMATICA
PrimeOmega[Numerator[Table[Sum[k/(n - k + 1), {k, 1, n}], {n, 1, 50}]]] (* G. C. Greubel, Jan 22 2017 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Nov 09 2006
STATUS
approved