

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
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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. 12 (1979), pp. 7180, alternative link.


EXAMPLE

3 is a term since 1 + A005361(1) = 2 and 2 + A005361(2) = 3 are not exceeding 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



