A003978 Möbius transform of A003964.

1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 14, 6, 8, 8, 21, 6, 29, 8, 12, 10, 41, 8, 20, 14, 18, 12, 55, 8, 76, 16, 20, 21, 24, 12, 100, 29, 28, 16, 134, 12, 175, 20, 24, 41, 230, 16, 42, 20, 42, 28, 296, 18, 40, 24, 58, 55, 384, 16, 489, 76, 36, 32, 56, 20, 626, 42, 82, 24, 791, 24

Offset

1,3

Links

Table of n, a(n) for n=1..72.

Formula

Multiplicative with a(p^e) = (q-1)q^(e-1) were q = partition(pi(p)+1) = A000041(A000720(p)+1). - David W. Wilson, Sep 01 2001

Mathematica

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

Crossrefs

Cf. A000041, A000720, A003964, A003979.

Sequence in context: A000010 A372681 A372677 * A122645 A372676 A122646

Adjacent sequences: A003975 A003976 A003977 * A003979 A003980 A003981

Keyword

nonn,easy,mult

Author

Marc LeBrun

Extensions

More terms from David W. Wilson, Aug 29 2001

Status

approved