A264859 a(n) is the denominator of c(n), where c(n) is calculated from Product_{i>=1}(1-c(i)*x^i) = exp(-(x^2)/(1-x))*(1-x).

1, 1, 1, 2, 1, 6, 1, 8, 3, 10, 1, 36, 1, 14, 15, 128, 1, 648, 1, 800, 21, 22, 1, 13824, 5, 26, 81, 6272, 1, 972000, 1, 32768, 33, 34, 35, 3359232, 1, 38, 39, 20480000, 1, 96018048, 1, 247808, 30375, 46, 1, 4586471424, 7, 500000, 51, 1384448, 1, 204073344, 55

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.

Links

Table of n, a(n) for n=1..55.

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

Cf. A259027 (numerators).

Sequence in context: A324370 A324193 A364829 * A007956 A107754 A181569

Adjacent sequences: A264856 A264857 A264858 * A264860 A264861 A264862

Keyword

nonn,frac

Author

Gevorg Hmayakyan, Nov 26 2015

Status

approved