OFFSET
1,5
REFERENCES
P. J. Cameron, Some counting problems related to permutation groups, Discrete Math., 225 (2000), 77-92.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
MAPLE
with(numtheory): ietr:= proc(p) local a, c; c:= proc(n) option remember; local j; n*p(n)-add(c(j)*p(n-j), j=1..n-1) end; a:=proc(n) option remember; local d; `if`(n=0, 1, add(mobius(n/d)*c(d), d=divisors(n))/n) end end: a:= ietr(n-> add(phi(d) *2^(n/d)/2/n, d=select(m-> modp(m, 2)=1, divisors(n)))): seq(a(n), n=1..40); # Alois P. Heinz, Sep 08 2008
# The function EulerInvTransform is defined in A358451.
a := EulerInvTransform(A000016):
seq(a(n), n = 1..39); # Peter Luschny, Nov 21 2022
MATHEMATICA
ietr[p_] := Module[{a, c}, c[n_] := c[n] = Module[{j}, n*p[n] - Sum[c[j]*p[n-j], {j, 1, n-1}]]; a[n_] := a[n] = Module[{d}, If[n == 0, 1, Sum[MoebiusMu[n/d]*c[d], {d, Divisors[n]}]/n]]; a]; a = ietr[Function[n, Sum[EulerPhi[d]*2^(n/d)/2/n, {d, Select[Divisors[n], OddQ]}]]]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jan 17 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 02 2000
EXTENSIONS
Better definition and more terms from Vladeta Jovovic, Mar 13 2008
STATUS
approved