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

%I A058199 #36 Jul 02 2025 16:02:00
%S A058199 4,6,12,12,24,30,36,60,60,60,120,120,120,180,180,180,240,240,360,360,
%T A058199 360,420,720,720,720,720,840,840,840,1260,1260,1260,1680,1680,1680,
%U A058199 1680,1680,2160,2520,2520,2520,2520,2520,2520,2520,2520,5040,5040,5040
%N A058199 Where d(m) (number of divisors, A000005) falls by at least n.
%C A058199 In the first 500 entries, only 3 entries (1, 2, and 25200) of A002182 are missed. - _Bill McEachen_, Nov 05 2020
%C A058199 a(n) exists for all n (Turán, 1954). - _Amiram Eldar_, Apr 13 2024
%D A058199 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 A058199 Amiram Eldar, <a href="/A058199/b058199.txt">Table of n, a(n) for n = 1..2014</a> (terms 1..500 from T. D. Noe)
%H A058199 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>.
%F A058199 A051950(a(n) + 1) <= - n. - _Reinhard Zumkeller_, Feb 04 2013
%e A058199 d(12) = 6, d(13) = 2 gives first drop of >= 3, so a(3) = a(4) = 12.
%t A058199 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 *)
%o A058199 (Haskell)
%o A058199 import Data.List (findIndex)
%o A058199 import Data.Maybe (fromJust)
%o A058199 a058199 n = fromJust $ findIndex (n <=) $ map negate a051950_list
%o A058199 -- _Reinhard Zumkeller_, Feb 04 2013
%Y A058199 Cf. A000005, A002182, A051950, A058197, A058198.
%K A058199 nonn,nice,easy
%O A058199 1,1
%A A058199 _N. J. A. Sloane_, Nov 28 2000
%E A058199 More terms from _James Sellers_, Nov 29 2000