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%I #16 May 15 2020 16:08:28
%S 0,1,1,1,2,3,2,2,1,1,1,1,2,1,3,1,2,2,3,5,3,3,2,3,2,2,3,3,4,1,1,2,2,1,
%T 2,1,2,2,1,2,2,1,4,1,4,3,3,2,1,2,5,2,3,3,2,1,2,1,1,2,2,4,3,2,4,3,4,2,
%U 1,3,1,3,4,2,2,4,5,7,3,3,1,2,3,4,1,1,3,5,2,1,2,1,2,5,4,6,2,3,1,2,3,2,4,3,1,1
%N a(n) = A001222(A048673(n)).
%H Antti Karttunen, <a href="/A286582/b286582.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A001222(A048673(n)).
%o (PARI)
%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of _Michel Marcus_
%o A048673(n) = (A003961(n)+1)/2;
%o A286582(n) = bigomega(A048673(n));
%o (Scheme) (define (A286582 n) (A001222 (A048673 n)))
%o (Python)
%o from sympy import factorint, nextprime, primefactors, prod
%o def a001222(n): return 0 if n==1 else a001222(n//primefactors(n)[-1]) + 1
%o def a048673(n):
%o f = factorint(n)
%o return 1 if n==1 else (1 + prod(nextprime(i)**f[i] for i in f))//2
%o def a(n): return a001222(a048673(n))
%o print([a(n) for n in range(1, 51)]) # _Indranil Ghosh_, Jun 12 2017
%Y Cf. A001222, A048673, A091304, A278224, A286583, A286584, A286585.
%K nonn
%O 1,5
%A _Antti Karttunen_, May 31 2017
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