A058198 - OEIS

%I #24 May 05 2024 19:57:39

%S 2,6,12,12,24,24,48,48,60,60,120,120,168,168,180,180,240,240,360,360,

%T 360,360,720,720,720,720,720,720,840,840,1260,1260,1260,1260,1680,

%U 1680,2520,2520,2520,2520,2520,2520,2520,2520,3360,3360,5040,5040,5040,5040

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

%C a(n) exists for all n (Turán, 1954). - _Amiram Eldar_, Apr 13 2024

%C a(n) >= A061799(n). - _David A. Corneth_, Apr 13 2024

%D 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.

%H David A. Corneth, <a href="/A058198/b058198.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1004 from T. D. Noe, terms 1005..2044 from Amiram Eldar)

%H Pál Turán, Problem 71, Matematikai Lapok, Vol. 5 (1954), p. 48, <a href="https://real-j.mtak.hu/9380">entire volume</a>; Solution to Problem 71, by Lajos Takács, ibid., Vol. 56, (1956), p. 154, <a href="https://real-j.mtak.hu/9386">entire volume</a>.

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

%o (Haskell)

%o a058198 = (+ 1) . a058197  -- _Reinhard Zumkeller_, Feb 04 2013

%Y Equals A058197(n) + 1.

%Y Cf. A000005, A051950, A058199, A061799.

%K nonn,nice,easy

%O 1,1

%A _N. J. A. Sloane_, Nov 28 2000

%E More terms from _James A. Sellers_, Nov 29 2000