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A014665
Number of new fractions m/n < 1, where (m,n)=1 and "new" means the value of m*n has not occurred before.
5
1, 1, 2, 2, 4, 1, 6, 4, 6, 2, 10, 3, 12, 3, 5, 8, 16, 3, 18, 6, 7, 5, 22, 5, 20, 6, 18, 8, 28, 4, 30, 16, 12, 8, 18, 9, 36, 9, 14, 12, 40, 6, 42, 13, 17, 11, 46, 11, 42, 10, 19, 15, 52, 9, 25, 20, 21, 14, 58, 10, 60, 15, 28, 32, 29, 9, 66, 21, 26, 11, 70, 20, 72, 18, 23, 23, 42, 11, 78, 23, 54
OFFSET
1,3
REFERENCES
S. W. Golomb, personal communication, Svalbard, Norway, 7/97.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe).
EXAMPLE
{1}, {1/2}, {1/3,2/3}, {1/4,3/4}, {1/5,...,4/5}, {5/6}, ...
MATHEMATICA
a[1] = 1;
a[n_] := Sum[Boole[GCD[i, n] == 1 && Sum[t = i*n/d; Boole[GCD[t, d] == 1 && t < d < n], {d, Divisors[i*n]}] == 0], {i, 1, n - 1}];
Array[a, 100] (* Jean-François Alcover, Sep 05 2019, from PARI *)
PROG
(PARI) a(n)=if(n==1, 1, sum(i=1, n-1, gcd(i, n) == 1 && 0==sumdiv(i*n, d, my(t=i*n/d); gcd(t, d)==1 && d<n && t<d))) \\ Andrew Howroyd, Nov 16 2018
CROSSREFS
Sequence in context: A299020 A343505 A365687 * A055035 A235138 A346244
KEYWORD
nonn
EXTENSIONS
Example corrected by and more terms from Olivier Gérard, February 1999
STATUS
approved