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A286627 a(n) = exponent of the highest power of A000005(n) (number of divisors of n) dividing A000010(n) (totient function phi), a(1) = 1.

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%I A286627 #16 Jul 02 2017 03:59:20
%S A286627 1,0,1,0,2,0,1,1,1,1,1,0,2,0,1,0,4,1,1,0,1,0,1,1,0,1,0,1,2,1,1,0,1,2,
%T A286627 1,0,2,0,1,1,3,0,1,0,1,0,1,0,1,0,2,1,2,0,1,1,1,1,1,0,2,0,2,0,2,0,1,0,
%U A286627 1,1,1,1,3,1,0,2,1,1,1,0,0,1,1,1,3,0,1,1,3,1,1,0,1,0,1,0,5,1,1,0,2,1,1,1,1,1,1,1,2,1,1,0,4,0,1,0,2,0,2,1,0
%N A286627 a(n) = exponent of the highest power of A000005(n) (number of divisors of n) dividing A000010(n) (totient function phi), a(1) = 1.
%C A286627 a(1) = 1 by convention.
%H A286627 Antti Karttunen, <a href="/A286627/b286627.txt">Table of n, a(n) for n = 1..10000</a>
%F A286627 a(n) = A286561(A000010(n), A000005(n)).
%e A286627 A000005(5) = 2, A000010(5) = 4, 2^2 is the highest power of 2 which divides 4, thus a(5) = 2.
%e A286627 A000005(6) = 4, A000010(6) = 2, 4^0 = 1 is the highest power of 4 which divides 2, thus a(6) = 0.
%o A286627 (PARI) A286627(n) = valuation(eulerphi(n), numdiv(n));
%Y A286627 Cf. A000005, A000010, A286561, A286628, A289276.
%Y A286627 Cf. A015733 (positions of zeros), A020491 (of nonzeros).
%K A286627 nonn
%O A286627 1,5
%A A286627 _Antti Karttunen_, Jun 30 2017