

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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



