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

1,2

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.

Example

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

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

Cf. A005361.

Sequence in context: A235045 A235032 A242925 * A214913 A052499 A104739

Adjacent sequences: A336441 A336442 A336443 * A336445 A336446 A336447

Keyword

nonn

Author

Amiram Eldar, Jul 21 2020

Status

approved