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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 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

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