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 A117109 Moebius transform of binomial(n+3, 4). 1
 1, 4, 14, 30, 69, 107, 209, 295, 480, 641, 1000, 1209, 1819, 2166, 2976, 3546, 4844, 5379, 7314, 8110, 10402, 11645, 14949, 15890, 20405, 21927, 26910, 29055, 35959, 37108, 46375, 48484, 57890, 61196, 73536, 75027, 91389, 93951, 110096, 114260 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Partial sums of a(n) give A015650(n). LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = |{(x,y,z,w) : 1 <= x <= y <= z <= w <= n, gcd(x,y,z,w,n) = 1}|. G.f.: Sum_{k>=1} mu(k) * x^k / (1 - x^k)^5. - Ilya Gutkovskiy, Feb 13 2020 EXAMPLE a(2)=4 because of the quadruples (1,1,1,1), (1,1,1,2), (1,1,2,2), (1,2,2,2). MAPLE b34:= unapply(expand(binomial(n+3, 4)), n): f:= proc(n) local k; uses numtheory; add(b34(k)*mobius(n/k), k=divisors(n)) end proc: map(f, [\$1..100]); # Robert Israel, May 24 2019 PROG (PARI) a(n) = sumdiv(n, k, binomial(k+3, 4)*moebius(n/k)); \\ Michel Marcus, Nov 04 2018 CROSSREFS Cf. A007438, A015650, A117108. Sequence in context: A103779 A049451 A079776 * A317031 A140063 A051409 Adjacent sequences:  A117106 A117107 A117108 * A117110 A117111 A117112 KEYWORD nonn,changed AUTHOR Steve Butler, Apr 18 2006 STATUS approved

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Last modified February 18 00:37 EST 2020. Contains 332006 sequences. (Running on oeis4.)