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

%I A097296 #19 May 23 2024 04:26:36
%S A097296 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,
%T A097296 37,38,41,43,44,46,47,48,52,53,56,58,59,61,62,67,68,70,71,73,74,76,79,
%U A097296 82,83,86,89,92,94,97,101,103,105,106,107,109,110,113,116,118,122,124,127,130
%N A097296 Numbers k such that A001055(k) divides k.
%H A097296 Amiram Eldar, <a href="/A097296/b097296.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Alois P. Heinz)
%H A097296 Florian Luca, Anirban Mukhopadhyay and Kotyada Srinivas, <a href="http://arxiv.org/abs/0807.0986">On the Oppenheim's "factorisatio numerorum" function</a>, arXiv:0807.0986 [math.NT], 2008.
%F A097296 Luca et al. estimate the density of this sequence (see their Theorem 3).
%F A097296 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
%p A097296 g:= proc(n, k) option remember; `if`(n>k, 0, 1)+
%p A097296       `if`(isprime(n), 0, add(`if`(d>k, 0, g(n/d, d)),
%p A097296          d=numtheory[divisors](n) minus {1, n}))
%p A097296     end:
%p A097296 a:= proc(n) option remember; local k;
%p A097296       for k from 1+`if`(n=1, 0, a(n-1))
%p A097296       while irem(k, g(k$2))>0 do od; k
%p A097296     end:
%p A097296 seq(a(n), n=1..100);  # _Alois P. Heinz_, May 16 2014
%t A097296 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_ *)
%Y A097296 Cf. A001055.
%K A097296 nonn
%O A097296 1,2
%A A097296 _N. J. A. Sloane_, Jun 12 2009