OFFSET
1,2
COMMENTS
Erdős (1979) proved that the asymptotic density of this sequence is positive.
The numbers of terms not exceeding 10^k for k = 1, 2, ... are 7, 44, 307, 2778, 26808, 265339, 2645683, 26433775, 264269957, 2642484069, ... Apparently the asymptotic density of this sequence is about 0.2642...
REFERENCES
József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004. See chapter 4, p. 333.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul Erdős, Some unconventional problems in number theory, Acta Mathematica Academiae Scientiarum Hungarica, Vol. 33, No. 1-2 (1979), pp. 71-80, alternative link.
MATHEMATICA
b[1] = 1; b[n_] := Times @@ FactorInteger[n][[;; , 2]]; f[n_] := n + b[n]; fm = 0; s = {1}; Do[fm = Max[fm, f[n]]; If[n + 1 >= fm, AppendTo[s, n + 1]], {n, 1, 160}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 21 2020
STATUS
approved