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A071778 Number of ordered triples (a, b, c) with gcd(a, b, c) = 1 and 1 <= {a, b, c} <= n. 9
1, 7, 25, 55, 115, 181, 307, 439, 637, 841, 1171, 1447, 1915, 2329, 2881, 3433, 4249, 4879, 5905, 6745, 7861, 8911, 10429, 11557, 13297, 14773, 16663, 18355, 20791, 22495, 25285, 27541, 30361, 32905, 36289, 38845, 42841, 46027, 49987, 53395 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

IBM Ponder This, Jun 01 2002

Eric Weisstein's World of Mathematics, Greatest Common Divisor

FORMULA

a(n) = Sum(k=1..n, mu(k)*floor(n/k)^3). - Benoit Cloitre, May 11 2003

a(n) = n^3 - Sum(j=2..n, a(floor(n/j))). - Vladeta Jovovic, Nov 30 2004

MAPLE

f:=proc(n) local i, j, k, t1, t2, t3; t1:=0; for i from 1 to n do for j from 1 to n do t2:=gcd(i, j); for k from 1 to n do t3:=gcd(t2, k); if t3 = 1 then t1:=t1+1; fi; od: od: od: t1; end;

MATHEMATICA

a[n_] := Sum[MoebiusMu[k]*Quotient[n, k]^3, {k, 1, n}]; Array[a, 40] (* Jean-Fran├žois Alcover, Apr 14 2014, after Benoit Cloitre *)

PROG

(Java) public class Triples { public static void main(String[] argv) { int i, j, k, a, m, n, d; boolean cf; try {a = Integer.parseInt(argv[0]); } catch (Exception e) {a = 10; }

for (m = 1; m <= a; m++) { n = 0; for (i = 1; i <= m; i++) for (j = 1; j <= m; j++) for (k = 1; k <= m; k++) { cf = false; for (d = 2; d <= m; d++) cf = cf || ((i % d == 0) && (j % d == 0) && (k % d == 0)); if (!cf) n++; } System.out.println(m + ": " + n); } } }

(PARI) a(n)=sum(k=1, n, moebius(k)*(n\k)^3)

CROSSREFS

Cf. A018805 (ordered pairs).

Sequence in context: A155286 A155313 A213390 * A155250 A155260 A155244

Adjacent sequences:  A071775 A071776 A071777 * A071779 A071780 A071781

KEYWORD

nonn,changed

AUTHOR

Michael Malak (mmalak(AT)alum.mit.edu), Jun 04 2002

STATUS

approved

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Last modified April 20 05:52 EDT 2014. Contains 240779 sequences.