A103449 Values of k such that Sum_{m=0..k} Moebius(binomial(k,m)) = 0.

3, 12, 24, 29, 34, 40, 54, 60, 67, 68, 75, 86, 93, 97, 102, 119, 125, 131, 133, 142, 152, 157, 160, 163, 164, 168, 170, 172, 189, 193, 197, 208, 210, 220, 221, 228, 229, 246, 251, 255, 257, 261, 270, 275, 280, 293, 296, 307, 308, 313, 315, 332, 337, 338, 340

Offset

1,1

Comments

Values of k such that A103448(k) = 0.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Example

12 belongs to the sequence because the only squarefree values of binomial(12,m) are 1, 2*3*11, 2*3*11, 1, on which the Mobius function takes the values 1,-1,-1,1, respectively.
8 does not belong to the sequence because the only squarefree value of binomial(8,m) are 1, 2*5*7, 1, on which the Moebius function takes the values 1,-1,1, respectively.

Mathematica

A103448[n_]:= A103448[n]= Sum[MoebiusMu[Binomial[n, k]], {k, 0, n}];
f:= Table[A103448[n], {n, 0, 1050}];
Select[Range[0, 1000], f[[#]] == 0 &] - 1  (* G. C. Greubel, Jun 17 2021 *)

Prog

(PARI) is(k) = sum(m=0, k, moebius(binomial(k, m)))==0 \\ Felix Fröhlich, Jun 18 2021

Crossrefs

Cf. A008683, A103447, A103448.

Sequence in context: A354529 A242636 A012469 * A030571 A297675 A112236

Adjacent sequences: A103446 A103447 A103448 * A103450 A103451 A103452

Keyword

nonn

Author

Emeric Deutsch, Feb 07 2005

Status

approved