

A058197


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


4



1, 5, 11, 11, 23, 23, 47, 47, 59, 59, 119, 119, 167, 167, 179, 179, 239, 239, 359, 359, 359, 359, 719, 719, 719, 719, 719, 719, 839, 839, 1259, 1259, 1259, 1259, 1679, 1679, 2519, 2519, 2519, 2519, 2519, 2519, 2519, 2519, 3359, 3359, 5039, 5039, 5039, 5039
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OFFSET

1,2


REFERENCES

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section II.1.3.a.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1004


FORMULA

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


EXAMPLE

d(11)=2, d(12)=6 gives first jump of >= 3, so a(3)=a(4)=11.


MATHEMATICA

d[m_] := d[m] = DivisorSigma[0, m]; td = Table[d[m]  d[m1], {m, 2, 6000}]; a[n_] := Position[td, j_ /; j >= n, 1][[1, 1]]; Table[a[n], {n, Max[td]}] (* JeanFrançois Alcover, Nov 02 2011 *)
With[{d=Differences[DivisorSigma[0, Range[5100]]]}, Flatten[Table[ Position[ d, _?(#>=n&), {1}, 1], {n, 50}]]] (* Harvey P. Dale, Oct 02 2015 *)


PROG

(Haskell)
import Data.List (findIndex)
import Data.Maybe (fromJust)
a058197 n = (+ 1) $ fromJust $ findIndex (n <=) $ tail a051950_list
 Reinhard Zumkeller, Feb 04 2013


CROSSREFS

Equals A058198(n)  1.
Cf. A058199.
Sequence in context: A060846 A113002 A179618 * A289464 A289580 A126243
Adjacent sequences: A058194 A058195 A058196 * A058198 A058199 A058200


KEYWORD

nonn,nice,easy


AUTHOR

N. J. A. Sloane, Nov 28 2000


EXTENSIONS

More terms from James A. Sellers, Nov 29 2000


STATUS

approved



