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A015614 Sum( phi(i), i=1..n) - 1. 18
0, 1, 3, 5, 9, 11, 17, 21, 27, 31, 41, 45, 57, 63, 71, 79, 95, 101, 119, 127, 139, 149, 171, 179, 199, 211, 229, 241, 269, 277, 307, 323, 343, 359, 383, 395, 431, 449, 473, 489, 529, 541, 583, 603, 627, 649, 695, 711, 753, 773, 805, 829, 881, 899, 939, 963 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Number of elements in the set {(x,y): 1<=x<y<=n, 1=gcd(x,y)}. - Michael Somos, Jun 13 1999

Number of fractions in (Haros)-Farey series of order n.

The asymptotic limit for the sequence is a(n) ~ 3*n^2/Pi^2. - Martin Renner, Dec 12 2011

For n > 1: A214803(a(n)) = A165900(n-1). - Reinhard Zumkeller, Jul 29 2012

REFERENCES

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 170-171.

James J. Sylvester, On the number of fractions contained in any Farey series of which the limiting number is given, in: London, Edinburgh and Dublin Philosophical Magazine (5th series) 15 (1883), p. 251.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A002088(n) - 1.

a(n) = (A018805(n) - 1)/2. - Reinhard Zumkeller, Apr 08 2006

a(n) = A018805(n) - A002088a(n). - Reinhard Zumkeller, Jan 21 2013

EXAMPLE

x^2 + 3*x^3 + 5*x^4 + 9*x^5 + 11*x^6 + 17*x^7 + 21*x^8 +27*x^9 + ...

MATHEMATICA

Table[Sum[EulerPhi[m], {m, 1, n}]-1, {n, 1, 56}] (* Geoffrey Critzer, May 16 2014 *)

PROG

(Haskell)

a015614 = (subtract 1) . a002088  -- Reinhard Zumkeller, Jul 29 2012

(PARI) {a(n) = if( n<1, 0, sum(k=1, n, eulerphi(k), -1))} /* Michael Somos, Sep 06 2013 */

CROSSREFS

Cf. A002088, A018805, column 2 of triangle A186974.

Sequence in context: A056533 A114186 A117992 * A138203 A225523 A007952

Adjacent sequences:  A015611 A015612 A015613 * A015615 A015616 A015617

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

More terms from Reinhard Zumkeller, Apr 08 2006

STATUS

approved

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Last modified July 22 18:10 EDT 2017. Contains 289671 sequences.