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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 (list; graph; refs; listen; history; text; internal format)
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[m-1], {m, 2, 6000}]; a[n_] := Position[td, j_ /; j >= n, 1][[1, 1]]; Table[a[n], {n, Max[td]}] (* Jean-Fran├žois 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

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Last modified December 8 04:46 EST 2019. Contains 329853 sequences. (Running on oeis4.)