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A117108 Moebius transform of tetrahedral numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..45.

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), A015634 (partial sums), A059358, A116963.

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

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Last modified April 2 19:05 EDT 2020. Contains 333190 sequences. (Running on oeis4.)