A105560 a(1) = 1, and for n >= 2, a(n) = prime(bigomega(n)), where prime(n) = A000040(n) and bigomega(n) = A001222(n).

1, 2, 2, 3, 2, 3, 2, 5, 3, 3, 2, 5, 2, 3, 3, 7, 2, 5, 2, 5, 3, 3, 2, 7, 3, 3, 5, 5, 2, 5, 2, 11, 3, 3, 3, 7, 2, 3, 3, 7, 2, 5, 2, 5, 5, 3, 2, 11, 3, 5, 3, 5, 2, 7, 3, 7, 3, 3, 2, 7, 2, 3, 5, 13, 3, 5, 2, 5, 3, 5, 2, 11, 2, 3, 5, 5, 3, 5, 2, 11, 7, 3, 2, 7, 3, 3, 3, 7, 2, 7, 3, 5, 3, 3, 3, 13, 2, 5, 5, 7

Offset: 1

Author

Cino Hilliard, May 03 2005

Keywords

• easy
• nonn

Comments

From Antti Karttunen, Jul 21 2014: (Start)

a(n) divides A122111(n), A242424(n), A243072(n), A243073(n) because a(n) divides all the terms in column n of A243070.

a(2n-1) divides A243505(n) and a(2n-1)^2 divides A122111(2n-1).

(End)

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001222, A006530, A008578, A243070, A242424, A243072, A243073, A122111, A243505.

Programs

Mathematica

Table[Prime[Sum[FactorInteger[n][[i,2]],{i,1,Length[FactorInteger[n]]}]],{n,2,40}] (* Stefan Steinerberger, May 16 2007 *)

PARI

d(n) = for(x=2,n,print1(prime(bigomega(x))","))

Python

from sympy import prime, primefactors
def a001222(n): return 0 if n==1 else a001222(n/primefactors(n)[0]) + 1
def a(n): return 1 if n==1 else prime(a001222(n)) # Indranil Ghosh, Jun 15 2017

Formula

a(1) = 1, and for n >= 2, a(n) = A000040(A001222(n)).

From Antti Karttunen, Jul 21 2014: (Start)

a(n) = A008578(1 + A001222(n)).

a(n) = A006530(A122111(n)).

a(n) = A122111(n) / A122111(A064989(n)).

a(2n-1) = A122111(2n-1) / A243505(n).

a(n) = A242424(n) / A064989(n).

(End)

Extensions

a(1) = 1 prepended by Antti Karttunen, Jul 21 2014