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A201557 Proper GA1 numbers: terms of A197638 with at least three prime divisors counted with multiplicity.

%I A201557 #30 May 09 2021 02:17:42
%S A201557 183783600,367567200,1396755360,1745944200,2327925600,3491888400,
%T A201557 6983776800,80313433200,160626866400,252706217563800,288807105787200,
%U A201557 336941623418400,404329948102080,505412435127600,673883246836800,1010824870255200,2021649740510400,112201560598327200
%N A201557 Proper GA1 numbers: terms of A197638 with at least three prime divisors counted with multiplicity.
%C A201557 Infinitely many terms are superabundant (SA) A004394; the smallest is 183783600.
%C A201557 Infinitely many terms are colossally abundant (CA) A004490; the smallest is 367567200.
%C A201557 Infinitely many terms are odd (and hence neither SA nor CA); the smallest is 1058462574572984015114271643676625.
%C A201557 See Section 5 of "On SA, CA, and GA numbers".
%C A201557 For additional terms, in factored form, see "Table of proper GA1 numbers up to 10^60", where SA and CA numbers are starred * and **.
%H A201557 Amiram Eldar, <a href="/A201557/b201557.txt">Table of n, a(n) for n = 1..18408</a> (from the J.-L. Nicolas's table)
%H A201557 G. Caveney, J.-L. Nicolas, and J. Sondow, <a href="http://www.integers-ejcnt.org/l33/l33.pdf">Robin's theorem, primes, and a new elementary reformulation of the Riemann Hypothesis</a>, Integers 11 (2011), article A33.
%H A201557 G. Caveney, J.-L. Nicolas and J. Sondow, <a href="http://arxiv.org/abs/1112.6010">On SA, CA, and GA numbers</a>, Ramanujan J., 29 (2012), 359-384 and arXiv:1112.6010.
%H A201557 J.-L. Nicolas, <a href="http://math.univ-lyon1.fr/~nicolas/GAnumbers.html">Computation of GA1 numbers</a>, 2011.
%H A201557 J.-L. Nicolas, <a href="http://math.univ-lyon1.fr/~nicolas/GA160">Table of proper GA1 numbers up to 10^60</a>, 2011.
%F A201557 A197638(n) if A001222(A197638(n)) > 2
%e A201557 183783600 = 2^4 * 3^3 * 5^2 * 7 * 11 * 13 * 17 is the smallest proper GA1 number.
%p A201557 See "Computation of GA1 numbers".
%Y A201557 Cf. A000203, A001222, A067698, A197638, A197639, A201558, A216436.
%K A201557 nonn
%O A201557 1,1
%A A201557 Geoffrey Caveney, Jean-Louis Nicolas, and _Jonathan Sondow_, Dec 03 2011