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
Keywords
Examples
1, 1/2, 1/3, 1/4, 1/6, 1/8, 1/12, 3/40, 1/15, 1/16, ...
Links
- J. Sondow and E. W. Weisstein, MathWorld: Smarandache Function
Programs
-
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 = Infinity; 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 *)
Comments