A097604 a(n) = floor( phi(n)*sqrt(2*n) ) - n.

0, 0, 1, 1, 7, 0, 15, 8, 16, 7, 35, 7, 48, 17, 28, 29, 76, 18, 91, 30, 56, 44, 126, 31, 116, 60, 105, 61, 184, 31, 205, 96, 129, 97, 165, 65, 272, 118, 172, 103, 321, 67, 346, 143, 182, 165, 398, 108, 366, 150, 272, 192, 482, 133, 364, 197, 327, 243, 571, 115, 601, 272, 341

Offset

1,5

Comments

This is known to be always >= 0, i.e. that n/phi(n) <= sqrt(2n) holds for all n. This is a consequence of the stronger inequality in A079530.

References

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 9.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Mathematica

Table[Floor[Sqrt[2*n]*EulerPhi[n]] - n, {n, 1, 100}] (* G. C. Greubel, Jan 14 2019 *)

Prog

(PARI) vector(100, n, (sqrt(2*n)*eulerphi(n))\1 -n) \\ G. C. Greubel, Jan 14 2019
(Magma) [Floor(Sqrt(2*n)*EulerPhi(n)) - n: n in [1..100]]; // G. C. Greubel, Jan 14 2019
(Sage) [floor(sqrt(2*n)*euler_phi(n)) - n for n in (1..100)] # G. C. Greubel, Jan 14 2019

Crossrefs

Cf. A079530, A097850.

Sequence in context: A331423 A240825 A243773 * A240816 A007393 A348516

Adjacent sequences: A097601 A097602 A097603 * A097605 A097606 A097607

Keyword

nonn

Author

N. J. A. Sloane, based on emails from Alonso del Arte and Jud McCranie, Aug 30 2004

Status

approved