A058198 Where d(m) (number of divisors, A000005) has risen by at least n.

2, 6, 12, 12, 24, 24, 48, 48, 60, 60, 120, 120, 168, 168, 180, 180, 240, 240, 360, 360, 360, 360, 720, 720, 720, 720, 720, 720, 840, 840, 1260, 1260, 1260, 1260, 1680, 1680, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 3360, 3360, 5040, 5040, 5040, 5040

Offset

1,1

Comments

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

a(n) >= A061799(n). - David A. Corneth, 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

David A. Corneth, Table of n, a(n) for n = 1..10000 (terms 1..1004 from T. D. Noe, terms 1005..2044 from Amiram Eldar)

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.

Example

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

Prog

(Haskell)
a058198 = (+ 1) . a058197  -- Reinhard Zumkeller, Feb 04 2013

Crossrefs

Equals A058197(n) + 1.

Cf. A000005, A051950, A058199, A061799.

Sequence in context: A057340 A092427 A379520 * A096075 A278256 A066791

Adjacent sequences: A058195 A058196 A058197 * A058199 A058200 A058201

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, Nov 28 2000

Extensions

More terms from James A. Sellers, Nov 29 2000

Status

approved