OFFSET
1,4
COMMENTS
c(1) = 1 and for n>1, c(n) satisfies Sum_{d|n} (1/d)*c(n/d)^d = 1 + 1/n.
c(p) = 1 for prime p and a(p) = 1 accordingly.
MAPLE
c := proc (n) option remember; 1+1/n-add(procname(n/d)^d/d, d = `minus`(numtheory:-divisors(n), {1})) end proc: c(1) := 1: a := denom(map(c, [`$`(1 .. 100)]));
MATHEMATICA
nmax = 100; Remove[c]; Subscript[c, 1] = 1; Do[Subscript[c, k] = Subscript[c, k] /. (Flatten[Solve[SeriesCoefficient[E^(-x^2/(1 - x))*(1 - x), {x, 0, k}] == Coefficient[Expand[Product[1 - Subscript[c, i]*x^i, {i, 1, k}]], x^k], Subscript[c, k]]]), {k, 2, nmax}]; Table[Subscript[c, n], {n, 1, nmax}] // Denominator (* Vaclav Kotesovec, Dec 12 2015 *)
PROG
(PARI) lista(nn) = {vc = vector(nn); vc[1] = 1; for (n=2, nn, vc[n] = 1+1/n - sumdiv(n, d, if (d==1, 0, (vc[n/d]^d)/d)); print1(denominator(vc[n]), ", "); ); } \\ Michel Marcus, Nov 27 2015
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Gevorg Hmayakyan, Nov 26 2015
STATUS
approved