A259027 a(n) is the numerator 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, 1, 1, 1, 1, 5, 2, 3, 1, 19, 1, 5, 7, 85, 1, 323, 1, 479, 11, 9, 1, 7855, 4, 11, 64, 3849, 1, 533387, 1, 22229, 19, 15, 23, 2144111, 1, 17, 23, 12790847, 1, 53953727, 1, 153845, 23146, 21, 1, 2785982603, 6, 269757, 31, 861171, 1, 110066119, 39

Offset

1,8

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 := numer(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}] // Numerator (* 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(numerator(vc[n]), ", "); ); } \\ Michel Marcus, Nov 27 2015

Crossrefs

Cf. A264859 (denominators).

Sequence in context: A369456 A178566 A155551 * A214064 A343486 A098584

Adjacent sequences: A259024 A259025 A259026 * A259028 A259029 A259030

Keyword

nonn,frac

Author

Gevorg Hmayakyan, Nov 27 2015

Status

approved