A102862 Numbers of prime factors of the sum of the first n primes.

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

Offset

1,3

Links

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

Formula

a(n) = A001222(A007504(n)). - Amiram Eldar, Mar 09 2020

Example

a(3) = 2 because 2+3+5 = 10 = 2*5.
a(5) = 3 because 2+3+5+7+11 = 28 = 2*2*7.

Mathematica

PrimeOmega @ Accumulate @ Select[Range[230], PrimeQ] (* Amiram Eldar, Mar 09 2020 *)
PrimeOmega[Accumulate[Prime[Range[110]]]] (* Harvey P. Dale, Dec 22 2022 *)

Prog

(PARI) for(n=1, 105, print1(bigomega(sum(k=1, n, prime(k))), ", ")) \\ Rick L. Shepherd, May 17 2005

Crossrefs

Cf. A001222, A007504.

Sequence in context: A369323 A342655 A161901 * A029331 A037269 A124579

Adjacent sequences: A102859 A102860 A102861 * A102863 A102864 A102865

Keyword

nonn

Author

Giovanni Teofilatto, Mar 01 2005

Extensions

More terms from Rick L. Shepherd, May 17 2005

Status

approved