A058199 Where d(m) (number of divisors, A000005) falls by at least n.

4, 6, 12, 12, 24, 30, 36, 60, 60, 60, 120, 120, 120, 180, 180, 180, 240, 240, 360, 360, 360, 420, 720, 720, 720, 720, 840, 840, 840, 1260, 1260, 1260, 1680, 1680, 1680, 1680, 1680, 2160, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 5040, 5040, 5040

Offset

1,1

Comments

In the first 500 entries, only 3 entries (1, 2, and 25200) of A002182 are missed. - Bill McEachen, Nov 05 2020

a(n) exists for all n (Turán, 1954). - Amiram Eldar, Apr 13 2024

References

József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter II, p. 39, section II.1.3.a.

Links

Amiram Eldar, Table of n, a(n) for n = 1..2014 (terms 1..500 from T. D. Noe)

Pál Turán, Problem 71, Matematikai Lapok, Vol. 5 (1954), p. 48, entire volume; Solution to Problem 71, by Lajos Takács, ibid., Vol. 56, (1956), p. 154, entire volume.

Formula

A051950(a(n) + 1) <= - n. - Reinhard Zumkeller, Feb 04 2013

Example

d(12) = 6, d(13) = 2 gives first drop of >= 3, so a(3) = a(4) = 12.

Mathematica

max = 10^4; dd = Differences[Table[DivisorSigma[0, m], {m, 1, max}]]; a[n_] := Position[dd, d_ /; d <= -n, 1, 1][[1, 1]]; Table[a[n], {n, 1, -Min[dd] }] (* Jean-François Alcover, Nov 23 2015 *)

Prog

(Haskell)
import Data.List (findIndex)
import Data.Maybe (fromJust)
a058199 n = fromJust $ findIndex (n <=) $ map negate a051950_list
-- Reinhard Zumkeller, Feb 04 2013

Crossrefs

Cf. A000005, A002182, A051950, A058197, A058198.

Sequence in context: A143356 A058270 A332934 * A289535 A310592 A310593

Adjacent sequences: A058196 A058197 A058198 * A058200 A058201 A058202

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, Nov 28 2000

Extensions

More terms from James A. Sellers, Nov 29 2000

Status

approved