A094404 Numerators of low-water marks of mu(n)/n, where mu(n) is A002034.

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,8

Comments

Denominators are A094372 and positions are A094371.

Links

Table of n, a(n) for n=1..105.

J. Sondow and E. W. Weisstein, MathWorld: Smarandache Function

Example

1, 1/2, 1/3, 1/4, 1/6, 1/8, 1/12, 3/40, 1/15, 1/16, ...

Mathematica

A002034[1] := 1; A002034[n_] := Max[A002034 @@@ FactorInteger[n]]; A002034[p_, 1] := p; A002034[p_, alpha_] := A002034[p, alpha] = Module[{a, k, r, i, nu, k0 = alpha(p - 1)}, i = nu = Floor[Log[p, 1 + k0]]; a[1] = 1; a[n_] := (p^n - 1)/(p - 1); k[nu] = Quotient[alpha, a[nu]]; r[nu] = alpha - k[nu]a[nu]; While[r[i] > 0, k[i - 1] = Quotient[r[i], a[i - 1]]; r[i - 1] = r[i] - k[i - 1]a[i - 1]; i-- ]; k0 + Plus @@ k /@ Range[i, nu]]; M = {}; a = 2; Do[ s = A002034[n]; If[s/n < a, a = s/n; AppendTo[M, a]]], {n, 40320}]; Numerator[M] (* Jonathan Sondow, Apr 28 2004, revised by Eric W. Weisstein, May 17 2004 *)

Crossrefs

Cf. A002034, A094371, A094372, A094634.

Sequence in context: A371149 A260196 A358692 * A361129 A103756 A103755

Adjacent sequences: A094401 A094402 A094403 * A094405 A094406 A094407

Keyword

nonn

Author

Eric W. Weisstein, Apr 29 2004

Status

approved