A000743 Number of compositions of n into 5 ordered relatively prime parts. (Formerly M3852 N1577)

1, 5, 15, 35, 70, 125, 210, 325, 495, 700, 1000, 1330, 1820, 2305, 3060, 3750, 4830, 5775, 7315, 8490, 10625, 12155, 14880, 16835, 20475, 22620, 27405, 30100, 35750, 39100, 46360, 49655, 58905, 62985, 73320, 78340, 91390, 95720, 111930, 117425

Offset

5,2

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Marius A. Burtea, Table of n, a(n) for n = 5..10000

H. W. Gould, Binomial coefficients, the bracket function and compositions with relatively prime summands, Fib. Quart. 2(4) (1964), 241-260.

N. J. A. Sloane, Transforms

Formula

Möbius transform of binomial(n-1, 4).

G.f.: Sum_{k>=1} mu(k) * x^(5*k) / (1 - x^k)^5. - Ilya Gutkovskiy, Feb 05 2020

Maple

with(numtheory):
a:= n-> add(mobius(n/d)*binomial(d-1, 4), d=divisors(n)):
seq(a(n), n=5..50);  # Alois P. Heinz, Feb 05 2020

Mathematica

a[n_] := Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k - 1, 4], {k, 1, n}]; Table[a[n], {n, 5, 52}] (* Jean-François Alcover, Feb 11 2016 *)

Prog

(Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 4):d in Divisors(n)]:n in[5..44]]; // Marius A. Burtea, Feb 08 2020

Crossrefs

Cf. A000741, A000742, A023031, A023032, A023033, A023034, A023035.

Sequence in context: A000750 A289389 A008487 * A138779 A341184 A090580

Adjacent sequences: A000740 A000741 A000742 * A000744 A000745 A000746

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Offset changed to 5 by Ilya Gutkovskiy, Feb 05 2020

Status

approved