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A319696 Number of distinct values obtained when Euler phi (A000010) is applied to the divisors of n. 6

%I

%S 1,1,2,2,2,2,2,3,3,2,2,3,2,2,4,4,2,3,2,4,4,2,2,4,3,2,4,4,2,4,2,5,4,2,

%T 4,5,2,2,4,5,2,4,2,4,6,2,2,5,3,3,4,4,2,4,4,6,4,2,2,5,2,2,5,6,4,4,2,4,

%U 4,4,2,7,2,2,6,4,4,4,2,6,5,2,2,6,4,2,4,6,2,6,4,4,4,2,4,6,2,3,6,6,2,4,2,6,8

%N Number of distinct values obtained when Euler phi (A000010) is applied to the divisors of n.

%H Antti Karttunen, <a href="/A319696/b319696.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A319695(n) + [n (mod 4) != 2], where [ ] is the Iverson bracket, resulting 0 when n = 2 mod 4, and 1 otherwise.

%e For n = 6, it has four divisors: 1, 2, 3 and 6, and applying A000010 to these gives 1, 1, 2, 2, with just two distinct values, thus a(6) = 2.

%o (PARI) A319696(n) = { my(m=Map(),s,k=0); fordiv(n,d,if(!mapisdefined(m,s=eulerphi(d)), mapput(m,s,s); k++)); (k); };

%Y Cf. A000010, A319695.

%Y Cf. also A184395, A319686.

%K nonn

%O 1,3

%A _Antti Karttunen_, Oct 02 2018

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Last modified December 6 16:24 EST 2019. Contains 329808 sequences. (Running on oeis4.)