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A319695 Number of distinct values obtained when Euler phi (A000010) is applied to proper divisors of n. 6

%I #8 Oct 02 2018 17:41:31

%S 0,1,1,1,1,2,1,2,2,2,1,2,1,2,3,3,1,3,1,3,3,2,1,3,2,2,3,3,1,4,1,4,3,2,

%T 3,4,1,2,3,4,1,4,1,3,5,2,1,4,2,3,3,3,1,4,3,5,3,2,1,4,1,2,4,5,3,4,1,3,

%U 3,4,1,6,1,2,5,3,3,4,1,5,4,2,1,5,3,2,3,5,1,6,3,3,3,2,3,5,1,3,5,5,1,4,1,5,7

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

%H Antti Karttunen, <a href="/A319695/b319695.txt">Table of n, a(n) for n = 1..65537</a>

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

%o (PARI) A319695(n) = { my(m=Map(),s,k=0); fordiv(n,d,if((d<n)&&!mapisdefined(m,s=eulerphi(d)), mapput(m,s,s); k++)); (k); };

%Y Cf. A000010, A319696.

%Y Cf. also A304793, A305611, A316555, A316556, A319685 for similarly constructed sequences.

%K nonn

%O 1,6

%A _Antti Karttunen_, Oct 02 2018

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)