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A306694 a(n) is the denominator of log(A014963(n))/log(n) if n > 1 and a(1) = 1.

%I A306694 #29 Nov 17 2019 15:58:29
%S A306694 1,1,1,2,1,1,1,3,2,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,2,1,3,1,1,1,1,5,1,1,
%T A306694 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,6,1,1,1,1,
%U A306694 1,1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
%N A306694 a(n) is the denominator of log(A014963(n))/log(n) if n > 1 and a(1) = 1.
%C A306694 Log(A112624(n)) is the inverse Möbius transform of log(a(n)).
%H A306694 Antti Karttunen, <a href="/A306694/b306694.txt">Table of n, a(n) for n = 1..100000</a>
%H A306694 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A306694 If n is a prime power (in the sense of A246655) then a(n) is the exponent of this prime and otherwise a(n) is 1. - _Peter Luschny_, Mar 18 2019
%F A306694 Dirichlet generating function: zeta(s) + Sum_{n>=1} n*primezeta((n + 1)*s). - _Mats Granvik_, Mar 24 2019
%p A306694 with(numtheory): pexp := n -> ifactors(n)[2][1][2]:
%p A306694 a := n -> if nops(factorset(n)) = 1 then pexp(n) else 1 fi:
%p A306694 seq(a(n), n=1..101); # _Peter Luschny_, Mar 19 2019
%t A306694 Table[Denominator[FullSimplify[MangoldtLambda[n]/Log[n]]], {n, 1, 101}]
%o A306694 (Sage)
%o A306694 def a(n):
%o A306694     F = n.factor()
%o A306694     return 1 if len(F) != 1 else F[0][1]
%o A306694 print([a(n) for n in (1..101)]) # _Peter Luschny_, Mar 18 2019
%o A306694 (PARI) A306694(n) = if((n=isprimepower(n))>0,n,1); \\ _Antti Karttunen_, Nov 17 2019
%Y A306694 Cf. A014963, A112624, A246655.
%K A306694 nonn
%O A306694 1,4
%A A306694 _Mats Granvik_, Mar 05 2019
%E A306694 Data section extended up to term a(121) by _Antti Karttunen_, Nov 17 2019