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A332559 a(n) = n + A332558(n) + 1.

%I A332559 #21 Jun 06 2021 02:53:58
%S A332559 6,6,6,8,10,12,12,12,15,15,18,18,20,20,20,24,24,24,24,24,28,30,30,30,
%T A332559 30,35,35,35,36,36,40,40,40,40,40,45,45,45,45,48,48,48,54,54,54,56,56,
%U A332559 56,56,60,60,60,60,60,60,63,70,70,70,70,70,70,70,72,72,72
%N A332559 a(n) = n + A332558(n) + 1.
%H A332559 Robert Israel, <a href="/A332559/b332559.txt">Table of n, a(n) for n = 1..10000</a>
%H A332559 J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, <a href="http://arxiv.org/abs/2004.14000">Three Cousins of Recaman's Sequence</a>, arXiv:2004:14000 [math.NT], April 2020.
%p A332559 f:= proc(n) local k,p;
%p A332559   p:= n;
%p A332559   for k from 1 do
%p A332559     p:= p*(n+k);
%p A332559     if (p/(n+k+1))::integer then return n+k+1 fi
%p A332559   od
%p A332559 end proc:
%p A332559 map(f, [$1..100]); # _Robert Israel_, Feb 25 2020
%t A332559 a[n_] := Module[{k, p = n}, For[k = 1, True, k++, p *= (n+k); If[Divisible[p, n+k+1], Return[n+k+1]]]];
%t A332559 Array[a, 100] (* _Jean-François Alcover_, Jul 18 2020, after Maple *)
%o A332559 (Python)
%o A332559 def a(n):
%o A332559     k, p = 1, n*(n+1)
%o A332559     while p%(n+k+1): k += 1; p *= (n+k)
%o A332559     return n + k + 1
%o A332559 print([a(n) for n in range(1, 67)]) # _Michael S. Branicky_, Jun 06 2021
%Y A332559 Cf. A061836, A332558, A332560, A332561.
%K A332559 nonn
%O A332559 1,1
%A A332559 _Scott R. Shannon_ and _N. J. A. Sloane_, Feb 24 2020