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A117109 Moebius transform of binomial(n+3, 4). 2

%I

%S 1,4,14,30,69,107,209,295,480,641,1000,1209,1819,2166,2976,3546,4844,

%T 5379,7314,8110,10402,11645,14949,15890,20405,21927,26910,29055,35959,

%U 37108,46375,48484,57890,61196,73536,75027,91389,93951,110096,114260

%N Moebius transform of binomial(n+3, 4).

%C Partial sums of a(n) give A015650(n).

%H Robert Israel, <a href="/A117109/b117109.txt">Table of n, a(n) for n = 1..10000</a>

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

%F G.f.: Sum_{k>=1} mu(k) * x^k / (1 - x^k)^5. - _Ilya Gutkovskiy_, Feb 13 2020

%e a(2)=4 because of the quadruples (1,1,1,1), (1,1,1,2), (1,1,2,2), (1,2,2,2).

%p b34:= unapply(expand(binomial(n+3,4)),n):

%p f:= proc(n) local k; uses numtheory;

%p add(b34(k)*mobius(n/k),k=divisors(n))

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, May 24 2019

%o (PARI) a(n) = sumdiv(n, k, binomial(k+3, 4)*moebius(n/k)); \\ _Michel Marcus_, Nov 04 2018

%Y Cf. A007438, A015650, A117108.

%K nonn

%O 1,2

%A _Steve Butler_, Apr 18 2006

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Last modified April 5 03:52 EDT 2020. Contains 333238 sequences. (Running on oeis4.)