A161606 a(n) = gcd(A008472(n), A001222(n)).

0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 5, 1, 1, 2, 3, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 5, 1, 1, 1, 3, 2, 3, 1, 1, 1, 1, 1, 4, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3

Offset: 1

Author

Leroy Quet, Jun 14 2009

Keywords

• nonn

Examples

			28 has a prime-factorization of: 2^2 * 7^1. The sum of the distinct primes dividing 28 is 2+7 = 9. The sum of the exponents in the prime-factorization of 28 is 2+1 = 3. a(28) therefore equals gcd(9,3) = 3.
		

Links

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

Crossrefs

Cf. A001222, A008472.

Programs

Maple

A008472 := proc(n) if n = 1 then 0 ; else add(p, p= numtheory[factorset](n)) ; end if ; end proc:
A161606 := proc(n) igcd(A008472(n),numtheory[bigomega](n)) ; end proc:
seq(A161606(n),n=2..80) ; # R. J. Mathar, Jul 08 2011

Mathematica

Table[GCD[DivisorSum[n, # &, PrimeQ], PrimeOmega@ n], {n, 105}] (* Michael De Vlieger, Jul 20 2017 *)

Python

from sympy import primefactors, gcd
def a001222(n): return 0 if n==1 else a001222(n//primefactors(n)[-1]) + 1
def a(n): return gcd(sum(primefactors(n)), a001222(n))
print([a(n) for n in range(1, 151)]) # Indranil Ghosh, Jul 20 2017

Scheme

(define (A161606 n) (gcd (A001222 n) (A008472 n))) ;; Antti Karttunen, Jul 20 2017

Extensions

Term a(1)=0 prepended and more terms computed by Antti Karttunen, Jul 20 2017