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A117108
Moebius transform of tetrahedral numbers.
7
1, 3, 9, 16, 34, 43, 83, 100, 155, 182, 285, 292, 454, 473, 636, 696, 968, 929, 1329, 1304, 1678, 1735, 2299, 2136, 2890, 2818, 3489, 3484, 4494, 4052, 5455, 5168, 6250, 6168, 7652, 6988, 9138, 8547, 10196, 9840, 12340, 10954, 14189, 13140, 15380
OFFSET
1,2
COMMENTS
Partial sums of a(n) give A015634(n).
See also A059358, A116963 (applied to shifted version of tetrahedral numbers), inverse Moebius transform of tetrahedral numbers. - Jonathan Vos Post, Apr 20 2006
LINKS
FORMULA
a(n) = |{(x,y,z) : 1 <= x <= y <= z <= n, gcd(x,y,z,n) = 1}|.
G.f.: Sum_{k>=1} mu(k) * x^k / (1 - x^k)^4. - Ilya Gutkovskiy, Feb 13 2020
EXAMPLE
a(2)=3 because of the triples (1,1,1), (1,1,2), (1,2,2).
PROG
(PARI) a(n) = sumdiv(n, d, binomial(d+2, 3)*moebius(n/d)); \\ Michel Marcus, Nov 04 2018
CROSSREFS
Cf. A000292 (tetrahedral numbers), A007438, A008683, A015634 (partial sums), A059358, A116963, A117109, A343544.
Sequence in context: A232167 A058538 A197531 * A223188 A145796 A056403
KEYWORD
nonn
AUTHOR
Steve Butler, Apr 18 2006
EXTENSIONS
Offset changed to 1 by Ilya Gutkovskiy, Feb 13 2020
STATUS
approved