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A096216
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a(n) = number of terms among {a(1),a(2),a(3),...a(n-1)} which are coprime to n; a(1)=1.
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10
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1, 1, 2, 2, 4, 2, 6, 2, 7, 3, 10, 3, 12, 4, 9, 6, 16, 3, 18, 7, 10, 8, 22, 4, 22, 8, 18, 6, 28, 4, 30, 8, 19, 9, 28, 5, 36, 10, 25, 10, 40, 5, 42, 13, 22, 14, 46, 9, 42, 12, 33, 15, 52, 9, 40, 16, 35, 19, 58, 7, 60, 21, 33, 23, 49, 14, 66, 25, 42, 15, 70, 15, 72, 28, 34, 26, 55, 15, 78
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A family of related sequences can be generated using different positive integers for a(1).
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FORMULA
| If, for a given fixed a(1), b(n, j) = number of a(k)'s which are multiples of j, for 1 <= k <= n-1, then: a(n) = sum{j|n} mu(j) *b(n, j), where mu(j) is the Moebius (Mobius) function.
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EXAMPLE
| a(1)=1, a(2)=1 and a(9)=7 are those terms, prior to a(10), which are coprime with 10. So a(10) = 3.
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MAPLE
| a[1]:=1: for n from 2 to 100 do B:=[seq(gcd(n, a[j]), j=1..n-1)]; s:=0: for i from 1 to n-1 do if B[i]=1 then s:=s+1 else s:=s: fi: od: a[n]:=s: od: seq(a[n], n=1..85); (Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 01 2005)
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MATHEMATICA
| a[1] = 1; a[n_] := a[n] = Count[ GCD[ Table[ a[i], {i, n - 1}], n], 1]; Table[ a[n], {n, 80}] (from Robert G. Wilson v Jul 30 2004)
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PROG
| (PERL) #!/usr/bin/perl -w # from Hugo van der Sanden, hv(AT)crypt.org, Mar 30 2006
use bigint; # only because it is an easy way to get gcd()
$| = $n = 1;
@a = (0);
while (1) {
$v = grep $n->bgcd($_) == 1, @a;
print $a[ $n++ ] = $v, " ";
}
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CROSSREFS
| Cf. A056149, A116537.
Sequence in context: A127835 A117004 A128982 * A121599 A080221 A137849
Adjacent sequences: A096213 A096214 A096215 * A096217 A096218 A096219
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Jul 28 2004
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 30 2004
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