A003976 Möbius transform of A003963 (with alternate 0's omitted).

1, 1, 2, 3, 2, 4, 5, 2, 6, 7, 3, 8, 6, 4, 9, 10, 4, 6, 11, 5, 12, 13, 4, 14, 12, 6, 15, 8, 7, 16, 17, 6, 10, 18, 8, 19, 20, 6, 12, 21, 8, 22, 12, 9, 23, 15, 10, 14, 24, 8, 25, 26, 6, 27, 28, 11, 29, 16, 10, 18, 20, 12, 18, 30, 13, 31, 21, 8, 32, 33, 14, 20, 18, 12, 34, 35, 12, 20

Offset

1,3

Links

Table of n, a(n) for n=1..78.

N. J. A. Sloane, Transforms.

Formula

Multiplicative with a(p^e) = (q-1)q^(e-1) where q = pi(p) = A000720(p). - David W. Wilson, Sep 01 2001

Example

The Möbius transform begins 1,0,1,0,2,0,3,0,2,0,4,0,5,0,2,0,6,0,7,0,...

Mathematica

f[p_, e_] := Module[{q = PrimePi[p]}, (q-1)q^(e-1)]; a[n_] := Times @@ f @@@ FactorInteger[2*n-1]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Sep 04 2023 *)

Prog

(PARI) a(n) = {my(f=factor(2*n-1)); for (i=1, #f~, q = primepi(f[i, 1]); f[i, 1] = (q-1)*q^(f[i, 2]-1); f[i, 2] = 1); factorback(f); } \\ Michel Marcus, Feb 27 2015

Crossrefs

Cf. A000720, A003963.

Sequence in context: A136181 A265110 A304742 * A252371 A275817 A286533

Adjacent sequences: A003973 A003974 A003975 * A003977 A003978 A003979

Keyword

nonn,easy,mult

Author

Marc LeBrun

Extensions

More terms from David W. Wilson, Aug 29 2001

Status

approved