A070243 a(n) = Card{ k, phi(k) <= n }.

2, 5, 5, 9, 9, 13, 13, 18, 18, 20, 20, 26, 26, 26, 26, 32, 32, 36, 36, 41, 41, 43, 43, 53, 53, 53, 53, 55, 55, 57, 57, 64, 64, 64, 64, 72, 72, 72, 72, 81, 81, 85, 85, 88, 88, 90, 90, 101, 101, 101, 101, 103, 103, 105, 105, 108, 108, 110, 110, 119, 119, 119, 119, 127, 127

Offset

1,1

References

G. Tenenbaum & Jie Wu, Exercices corrigés de théorie analytique et probabiliste des nombres, Collection SMF, Cours specialises, Numero 2, pp. 78-79.

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 115-118.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Matteo Caorsi, Sergio Cecotti, Geometric classification of 4d N=2 SCFTs, arXiv:1801.04542 [hep-th], 2018.

Formula

Lim_{n ->infinity} a(n)/n = zeta(2)zeta(3)/zeta(6) = 1.943596436820759205057... = A082695.

a(n) = Sum_{k=1..n} A014197(k); a(n) = zeta(2)*zeta(3)/zeta(6)*n + O(n*exp(-c*sqrt(log(n))) for a suitable constant c > 0. - Benoit Cloitre, Apr 12 2003

Prog

(PARI) for(n=1, 150, print1(sum(i=1, 100*n, if(sign(eulerphi(i)-n)+1, 0, 1)+if((eulerphi(i)-n), 0, 1)), ", "))

Crossrefs

Sequence in context: A200242 A062553 A126357 * A367642 A050175 A243333

Adjacent sequences: A070240 A070241 A070242 * A070244 A070245 A070246

Keyword

easy,nonn

Author

Benoit Cloitre, May 11 2002

Status

approved