A097296 Numbers k such that A001055(k) divides k.

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 17, 19, 20, 22, 23, 26, 27, 28, 29, 30, 31, 34, 36, 37, 38, 41, 43, 44, 46, 47, 48, 52, 53, 56, 58, 59, 61, 62, 67, 68, 70, 71, 73, 74, 76, 79, 82, 83, 86, 89, 92, 94, 97, 101, 103, 105, 106, 107, 109, 110, 113, 116, 118, 122, 124, 127, 130

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Alois P. Heinz)

Florian Luca, Anirban Mukhopadhyay and Kotyada Srinivas, On the Oppenheim's "factorisatio numerorum" function, arXiv:0807.0986 [math.NT], 2008.

Formula

Luca et al. estimate the density of this sequence (see their Theorem 3).

The number of terms that do not exceed x is ~ x/(log(x))^(1+o(1)) (Luca et al., 2008). - Amiram Eldar, May 23 2024

Maple

g:= proc(n, k) option remember; `if`(n>k, 0, 1)+
      `if`(isprime(n), 0, add(`if`(d>k, 0, g(n/d, d)),
         d=numtheory[divisors](n) minus {1, n}))
    end:
a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 0, a(n-1))
      while irem(k, g(k$2))>0 do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, May 16 2014

Mathematica

g[n_, k_] := g[n, k] = If[n > k, 0, 1] + If[PrimeQ[n], 0, Sum[If[d > k, 0, g[n/d, d]], {d, Divisors[n] // Most // Rest}]]; a[1] = 1; a[n_] := (For[k = 1 + If[n == 1, 0, a[n-1]], Mod[k, g[k, k]] > 0 , k++]; k); Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 07 2014, after Alois P. Heinz *)

Crossrefs

Cf. A001055.

Sequence in context: A279455 A050687 A098908 * A131616 A175857 A173919

Adjacent sequences: A097293 A097294 A097295 * A097297 A097298 A097299

Keyword

nonn

Author

N. J. A. Sloane, Jun 12 2009

Status

approved