login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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, 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 (list; graph; refs; listen; history; text; internal format)
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: A111716 A178566 A155551 * A214064 A098584 A081750

Adjacent sequences:  A259024 A259025 A259026 * A259028 A259029 A259030

KEYWORD

nonn,frac

AUTHOR

Gevorg Hmayakyan, Nov 27 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 07:03 EST 2019. Contains 329978 sequences. (Running on oeis4.)