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A070633 a(n) is the number of k>0 such that phi(k) divides n. 4

%I #13 Sep 11 2018 17:02:34

%S 2,5,2,9,2,9,2,14,2,7,2,19,2,5,2,20,2,13,2,16,2,7,2,34,2,5,2,11,2,13,

%T 2,27,2,5,2,31,2,5,2,30,2,13,2,14,2,7,2,51,2,7,2,11,2,15,2,19,2,7,2,

%U 37,2,5,2,35,2,13,2,9,2,9,2,63,2,5,2,9,2,11,2,46,2,7,2,31,2,5,2,25,2,17,2

%N a(n) is the number of k>0 such that phi(k) divides n.

%C Inverse Möbius transform of A014197. - _Antti Karttunen_, Sep 10 2018

%H Antti Karttunen, <a href="/A070633/b070633.txt">Table of n, a(n) for n = 1..65537</a>

%F From _Antti Karttunen_, Sep 10 2018: (Start)

%F a(n) = Sum_{d|n} A014197(d).

%F a(n) >= A069932(n).

%F a(A000010(n)) = A071181(n).

%F (End)

%o (PARI) for(n=1,120,print1(sum(i=1,100*n,if(n%eulerphi(i),0,1)),","));

%o (PARI)

%o \\ In contrast to above program, this is safe in any range 1..n:

%o A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))}; \\ From A014197 by _M. F. Hasler_

%o A070633(n) = sumdiv(n, d, A014197(d)); \\ _Antti Karttunen_, Sep 10 2018

%Y Cf. A000010, A014197, A069932, A071181, A319048.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, May 13 2002

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Last modified June 10 09:13 EDT 2024. Contains 373259 sequences. (Running on oeis4.)