A336444 Numbers m such that k + A005361(k) <= m for all k < m.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 15, 16, 20, 22, 23, 24, 27, 30, 31, 32, 40, 43, 44, 47, 48, 52, 54, 59, 60, 62, 63, 70, 71, 72, 78, 79, 80, 86, 87, 88, 92, 94, 95, 96, 104, 107, 108, 116, 119, 120, 123, 124, 128, 135, 139, 140, 142, 143, 144, 152, 155, 156, 158

Offset: 1

Author

Amiram Eldar, Jul 21 2020

Keywords

• nonn

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...

Examples

			3 is a term since 1 + A005361(1) = 2 and 2 + A005361(2) = 3 do not exceed 3.
		

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.

Crossrefs

Cf. A005361.

Programs

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