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

%I A161606 #24 Apr 21 2021 11:25:26
%S A161606 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,
%T A161606 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,
%U A161606 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
%N A161606 a(n) = gcd(A008472(n), A001222(n)).
%H A161606 Antti Karttunen, <a href="/A161606/b161606.txt">Table of n, a(n) for n = 1..10000</a>
%e A161606 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.
%p A161606 A008472 := proc(n) if n = 1 then 0 ; else add(p, p= numtheory[factorset](n)) ; end if ; end proc:
%p A161606 A161606 := proc(n) igcd(A008472(n),numtheory[bigomega](n)) ; end proc:
%p A161606 seq(A161606(n),n=2..80) ; # _R. J. Mathar_, Jul 08 2011
%t A161606 Table[GCD[DivisorSum[n, # &, PrimeQ], PrimeOmega@ n], {n, 105}] (* _Michael De Vlieger_, Jul 20 2017 *)
%o A161606 (Scheme) (define (A161606 n) (gcd (A001222 n) (A008472 n))) ;; _Antti Karttunen_, Jul 20 2017
%o A161606 (Python)
%o A161606 from sympy import primefactors, gcd
%o A161606 def a001222(n): return 0 if n==1 else a001222(n//primefactors(n)[-1]) + 1
%o A161606 def a(n): return gcd(sum(primefactors(n)), a001222(n))
%o A161606 print([a(n) for n in range(1, 151)]) # _Indranil Ghosh_, Jul 20 2017
%Y A161606 Cf. A001222, A008472.
%K A161606 nonn
%O A161606 1,4
%A A161606 _Leroy Quet_, Jun 14 2009
%E A161606 Term a(1)=0 prepended and more terms computed by _Antti Karttunen_, Jul 20 2017