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

%I A105560 #31 Jun 15 2017 02:52:11
%S A105560 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,
%T A105560 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,
%U A105560 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
%N A105560 a(1) = 1, and for n >= 2, a(n) = prime(bigomega(n)), where prime(n) = A000040(n) and bigomega(n) = A001222(n).
%C A105560 From _Antti Karttunen_, Jul 21 2014: (Start)
%C A105560 a(n) divides A122111(n), A242424(n), A243072(n), A243073(n) because a(n) divides all the terms in column n of A243070.
%C A105560 a(2n-1) divides A243505(n) and a(2n-1)^2 divides A122111(2n-1).
%C A105560 (End)
%H A105560 Antti Karttunen, <a href="/A105560/b105560.txt">Table of n, a(n) for n = 1..10000</a>
%F A105560 a(1) = 1, and for n >= 2, a(n) = A000040(A001222(n)).
%F A105560 From _Antti Karttunen_, Jul 21 2014: (Start)
%F A105560 a(n) = A008578(1 + A001222(n)).
%F A105560 a(n) = A006530(A122111(n)).
%F A105560 a(n) = A122111(n) / A122111(A064989(n)).
%F A105560 a(2n-1) = A122111(2n-1) / A243505(n).
%F A105560 a(n) = A242424(n) / A064989(n).
%F A105560 (End)
%t A105560 Table[Prime[Sum[FactorInteger[n][[i,2]],{i,1,Length[FactorInteger[n]]}]],{n,2,40}] (* _Stefan Steinerberger_, May 16 2007 *)
%o A105560 (PARI) d(n) = for(x=2,n,print1(prime(bigomega(x))","))
%o A105560 (Python)
%o A105560 from sympy import prime, primefactors
%o A105560 def a001222(n): return 0 if n==1 else a001222(n/primefactors(n)[0]) + 1
%o A105560 def a(n): return 1 if n==1 else prime(a001222(n)) # _Indranil Ghosh_, Jun 15 2017
%Y A105560 Cf. A000040, A001222, A006530, A008578, A243070, A242424, A243072, A243073, A122111, A243505.
%K A105560 easy,nonn
%O A105560 1,2
%A A105560 _Cino Hilliard_, May 03 2005
%E A105560 a(1) = 1 prepended by _Antti Karttunen_, Jul 21 2014