A098035 -id:A098035 - cp's OEIS frontend

A098991 Numbers n where A098035(n)=0.

5, 9, 13, 15, 21, 27, 33, 35, 37, 39, 50, 55, 57, 61, 65, 73, 91, 93, 95, 111, 114, 115, 121, 122, 133, 141, 143, 145, 147, 155, 157, 170, 177, 183, 185, 189, 193, 195, 201, 205, 209, 213, 215, 217, 219, 231, 235, 247, 253, 259, 261, 277, 285, 295, 299, 301, 313

Offset: 1

Leroy Quet and Robert G. Wilson v, Nov 05 2004

nonn

Indranil Ghosh, Table of n, a(n) for n = 1..935 (terms < 5000)

Cf. A098035.

f[n_] := Plus @@ MoebiusMu[Divisors[n] + 1]; Select[ Range[319], f[ # ] == 0 &]

a(n) = sumdiv(n, k, moebius(k + 1));
for(n=1, 320, if(a(n) == 0, print1(n,", "))) \\ Indranil Ghosh, Mar 16 2017

Sum_{k|n} mu(k+1), where mu() is Moebius function.

A098018 a(n) = Sum_{k|n, k>=2} mu(k-1), where mu() is the Moebius function.

Original entry on oeis.org

0, 1, -1, 0, 0, -1, 1, -1, -1, 1, 1, -3, 0, 1, 0, 0, 0, -2, 0, -1, 0, 3, 1, -5, 0, 1, 0, 0, 0, -1, -1, -1, 0, 2, 2, -3, 0, 0, 0, -1, 0, -2, -1, 1, 0, 2, 1, -5, 1, 1, -1, 1, 0, -2, 1, 0, -1, 2, 1, -5, 0, -1, 1, -1, 0, 2, -1, 0, 0, 3, -1, -6, 0, 0, 1, -1, 2, 1, -1, -1, 0, 1, 1, -5, 0, 1, 0, 1, 0, -3, 1, 2, -2, 3, 1, -5, 0, 0, 0, -1, 0, -1, -1, -1, 2

Offset: 1

Leroy Quet, Oct 24 2004

sign

			12's divisors >=2 are 2, 3, 4, 6 and 12. So a(12) = mu(1) + mu(2) + mu(3) + mu(5) + mu(11) = 1 - 1 - 1 - 1 - 1 = -3.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A008683, A098035.

f[n_] := Plus @@ MoebiusMu[ Drop[ Divisors[n], 1] - 1]; Table[ f[n], {n, 105}] (* Robert G. Wilson v, Nov 01 2004 *)
Table[DivisorSum[n, MoebiusMu[# - 1] &, # > 1 &], {n, 105}] (* Michael De Vlieger, Sep 04 2017 *)

a(n)=sumdiv(n,k,if(k>1,moebius(k-1))) \\ Charles R Greathouse IV, Feb 07 2013

More terms from Robert G. Wilson v, Nov 01 2004

cp's OEIS Frontend

A098991 Numbers n where A098035(n)=0.

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