A341065 Number of ways to write n as an ordered sum of 5 squarefree numbers.

1, 5, 15, 30, 50, 76, 120, 180, 250, 315, 401, 520, 670, 805, 955, 1160, 1445, 1715, 1980, 2290, 2741, 3180, 3605, 4040, 4690, 5341, 5985, 6600, 7490, 8380, 9251, 10060, 11240, 12415, 13595, 14670, 16295, 17850, 19425, 20780, 22905, 24905, 26895, 28600, 31335, 33966, 36485, 38620

Offset

5,2

Links

Table of n, a(n) for n=5..52.

Formula

G.f.: (Sum_{k>=1} mu(k)^2 * x^k)^5.

Maple

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(n, 5):
seq(a(n), n=5..52);  # Alois P. Heinz, Feb 04 2021

Mathematica

nmax = 52; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 5] &

Crossrefs

Cf. A005117, A008683, A008966, A098235, A280210, A308840, A341064, A341066, A341067, A341068, A341069, A341070.

Sequence in context: A341984 A028895 A194150 * A246817 A010898 A048065

Adjacent sequences: A341062 A341063 A341064 * A341066 A341067 A341068

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2021

Status

approved