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A336444 Numbers m such that k + A005361(k) <= m for all k < m. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 21 2020
STATUS
approved

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Last modified July 20 23:17 EDT 2024. Contains 374461 sequences. (Running on oeis4.)