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A097850 a(n) = floor(2*sqrt(n)*phi(n)) - n. 2
1, 0, 3, 4, 12, 3, 24, 14, 27, 15, 55, 15, 73, 30, 46, 48, 114, 32, 137, 51, 88, 71, 188, 54, 175, 96, 160, 98, 272, 57, 303, 149, 196, 152, 248, 108, 400, 183, 260, 162, 471, 113, 507, 221, 276, 252, 583, 173, 539, 232, 406, 294, 704, 210, 538, 303, 486, 368, 832, 187, 876 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Always >= 0. But see A079530 and A097604 for stronger upper bounds on n/phi(n).

REFERENCES

David Burton, Elementary Number Theory" 4th edition, problem 7a in section 7.2 has the equivalent of n/phi(n) <= 2*sqrt(n). - Jud McCranie, Aug 30 2004

LINKS

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

MATHEMATICA

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

PROG

(PARI) vector(100, n, (2*sqrt(n)*eulerphi(n))\1 -n) \\ G. C. Greubel, Jan 14 2019

(MAGMA) [Floor(2*Sqrt(n)*EulerPhi(n)) - n: n in [1..100]]; // G. C. Greubel, Jan 14 2019

(Sage) [floor(2*sqrt(n)*euler_phi(n)) - n for n in (1..100)] # G. C. Greubel, Jan 14 2019

CROSSREFS

Cf. A079530, A097604.

Sequence in context: A042079 A045826 A084200 * A238855 A034854 A164982

Adjacent sequences:  A097847 A097848 A097849 * A097851 A097852 A097853

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 30 2004

STATUS

approved

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Last modified October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)