A076511 Numerator of cototient(n)/totient(n).

0, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 4, 7, 1, 1, 2, 1, 3, 3, 6, 1, 2, 1, 7, 1, 4, 1, 11, 1, 1, 13, 9, 11, 2, 1, 10, 5, 3, 1, 5, 1, 6, 7, 12, 1, 2, 1, 3, 19, 7, 1, 2, 3, 4, 7, 15, 1, 11, 1, 16, 3, 1, 17, 23, 1, 9, 25, 23, 1, 2, 1, 19, 7, 10, 17, 9, 1, 3, 1, 21, 1, 5, 21, 22, 31, 6, 1, 11, 19, 12, 11

Offset: 1

Author

Reinhard Zumkeller, Oct 15 2002

Keywords

• nonn
• frac

Links

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

Crossrefs

Cf. A076512 (denominators), A000010, A009195, A051953, A082695, A109395.

Programs

Mathematica

Table[Numerator[n/EulerPhi[n] - 1], {n, 1, 100}] (* Amiram Eldar, Nov 21 2022 *)

PARI

A076511(n) = numerator((n-eulerphi(n))/eulerphi(n)); \\ Antti Karttunen, Sep 07 2018

Formula

a(n) = A051953(n)/A009195(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A076512(k) = zeta(2)*zeta(3)/zeta(6) - 1 = A082695 - 1 = 0.943596... . Amiram Eldar, Nov 21 2022