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

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, 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, 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

Offset

1,1

Comments

Inverse Möbius transform of A014197. - Antti Karttunen, Sep 10 2018

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Formula

From Antti Karttunen, Sep 10 2018: (Start)

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

a(n) >= A069932(n).

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

(End)

Prog

(PARI) for(n=1, 120, print1(sum(i=1, 100*n, if(n%eulerphi(i), 0, 1)), ", "));
(PARI)
\\ In contrast to above program, this is safe in any range 1..n:
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
A070633(n) = sumdiv(n, d, A014197(d)); \\ Antti Karttunen, Sep 10 2018
(PARI) a(n) = sumdiv(n, d, invphiNum(d)); \\ Amiram Eldar, Nov 29 2024, using Max Alekseyev's invphi.gp

Crossrefs

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

Row lengths of A378638.

Sequence in context: A354709 A131711 A131201 * A266256 A247551 A347378

Adjacent sequences: A070630 A070631 A070632 * A070634 A070635 A070636

Keyword

easy,nonn

Author

Benoit Cloitre, May 13 2002

Status

approved