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A117109
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Moebius transform of binomial(n+3, 4).
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7
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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
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OFFSET
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1,2
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COMMENTS
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Partial sums of a(n) give A015650(n).
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LINKS
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FORMULA
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a(n) = |{(x,y,z,w) : 1 <= x <= y <= z <= w <= n, gcd(x,y,z,w,n) = 1}|.
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EXAMPLE
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a(2)=4 because of the quadruples (1,1,1,1), (1,1,1,2), (1,1,2,2), (1,2,2,2).
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MAPLE
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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:
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MATHEMATICA
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a[n_] := Sum[Binomial[k+3, 4] MoebiusMu[n/k], {k, Divisors[n]}];
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PROG
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(PARI) a(n) = sumdiv(n, k, binomial(k+3, 4)*moebius(n/k)); \\ Michel Marcus, Nov 04 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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