A117108 Moebius transform of tetrahedral numbers.

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

Seiichi Manyama, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A117105 A117106 A117107 * A117109 A117110 A117111

Keyword

nonn

Author

Steve Butler, Apr 18 2006

Extensions

Offset changed to 1 by Ilya Gutkovskiy, Feb 13 2020

Status

approved