cp's OEIS Frontend

A279930 Numbers which are highly composite and highly Brazilian.

%I A279930 #69 Jul 23 2020 12:01:44
%S A279930 1,24,60,120,180,360,720,840,1260,1680,2520,5040,7560,10080,15120,
%T A279930 20160,25200,27720,45360,50400,55440,83160,110880,166320,221760,
%U A279930 277200,332640,498960,554400,665280,720720,1081080,1441440,2162160,2882880
%N A279930 Numbers which are highly composite and highly Brazilian.
%C A279930 For a(6) = 360 to a(85) = 321253732800, the last term known today, there are 80 successive highly composite numbers that are also highly Brazilian numbers.
%C A279930 If beta(n) is the number of Brazilian representations of n, as in A284758, we have the following relations:
%C A279930 1) for a(k) = m with k <= 85 except 1, 9, 20 and 47, tau(m) = 2*beta(m) + 2, but,
%C A279930 2) for a(1) = 1, tau(1) = 2*beta(1) + 1, because beta(1) = 0, and,
%C A279930 3) for a(9) = 1260, a(20) = 50400 and a(47) = 4324320, tau(m) = 2*beta(m) + 4 because 1260 = 35*36, 50400 = 224*225 and 4324320 = 2079*2080 are oblong numbers.
%C A279930 These improved comments and the b-file come from the new terms in b-file of A066044 found by _Giovanni Resta_. - _Bernard Schott_, Aug 03 2019
%D A279930 D. Lignon, Dictionnaire de (presque) tous les nombres entiers, Editions Ellipses, 2012, page 420. [In French.]
%H A279930 Bernard Schott, <a href="/A279930/b279930.txt">Table of n, a(n) for n = 1..85</a>
%e A279930 360 is the 13th highly composite number and the 10th highly Brazilian number.
%e A279930 336 is the 9th highly Brazilian number, but is not a highly composite number since tau(336) = tau(240) = 20 and 240 is the 12th highly composite number.
%e A279930 240 is the 12th highly composite number, but is not a highly Brazilian number because beta(240) = beta(180) = 8 and 180 is the 8th highly Brazilian number.
%Y A279930 Intersection of A002182 (highly composite) and A329383 (highly Brazilian numbers).
%Y A279930 Cf. A284758.
%K A279930 nonn,base
%O A279930 1,2
%A A279930 _Bernard Schott_, Apr 12 2017
%E A279930 Typo in a(18) corrected by _J. Lowell_, Jul 08 2019
%E A279930 a(29)-a(35) from _Bernard Schott_, Jul 12 2019