%I #19 Apr 20 2021 06:58:38

%S 1,3,9,16,34,43,83,100,155,182,285,292,454,473,636,696,968,929,1329,

%T 1304,1678,1735,2299,2136,2890,2818,3489,3484,4494,4052,5455,5168,

%U 6250,6168,7652,6988,9138,8547,10196,9840,12340,10954,14189,13140,15380

%N Moebius transform of tetrahedral numbers.

%C Partial sums of a(n) give A015634(n).

%C See also A059358, A116963 (applied to shifted version of tetrahedral numbers), inverse Moebius transform of tetrahedral numbers. - _Jonathan Vos Post_, Apr 20 2006

%H Seiichi Manyama, <a href="/A117108/b117108.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = |{(x,y,z) : 1 <= x <= y <= z <= n, gcd(x,y,z,n) = 1}|.

%F G.f.: Sum_{k>=1} mu(k) * x^k / (1 - x^k)^4. - _Ilya Gutkovskiy_, Feb 13 2020

%e a(2)=3 because of the triples (1,1,1), (1,1,2), (1,2,2).

%o (PARI) a(n) = sumdiv(n, d, binomial(d+2, 3)*moebius(n/d)); \\ _Michel Marcus_, Nov 04 2018

%Y Cf. A000292 (tetrahedral numbers), A007438, A008683, A015634 (partial sums), A059358, A116963, A117109, A343544.

%K nonn

%O 1,2

%A _Steve Butler_, Apr 18 2006

%E Offset changed to 1 by _Ilya Gutkovskiy_, Feb 13 2020