A227314 Number of prime factors, with multiplicity, of the sum of the first n composite numbers.

2, 2, 3, 3, 1, 2, 3, 3, 2, 5, 4, 3, 3, 1, 6, 4, 1, 2, 2, 1, 6, 3, 2, 2, 2, 3, 2, 4, 4, 2, 2, 3, 8, 3, 1, 1, 1, 3, 2, 2, 2, 2, 1, 2, 3, 2, 1, 1, 3, 3, 4, 2, 1, 1, 3, 7, 7, 3, 2, 4, 4, 2, 1, 1, 2, 4, 2, 1, 3, 4, 4, 3, 1, 1, 1, 2, 5, 2, 3, 6, 2, 2, 3, 6, 5, 1, 5, 3, 2, 3, 2, 6, 7, 2, 2, 2, 6, 3, 2, 3

Offset: 1

Author

Jonathan Vos Post, Jul 06 2013

Keywords

• nonn
• easy

Examples

			a(10) = 5 because A053767(10) = 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 112 = 2^4 * 7, which has 5 prime factors, with multiplicity.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A002808, A053767.

Programs

Maple

A227314 := proc(n)
    A001222(A053767(n)) ;
end proc: # R. J. Mathar, Jul 06 2013

Mathematica

PrimeOmega[Accumulate[Select[Range[150], CompositeQ]]] (* Amiram Eldar, Oct 06 2024 *)

Formula

a(n) = A001222(A053767(n)).