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A307115 Primitive 5-abundant numbers: Numbers k such that sigma(k) > 5k (A215264) all of whose proper divisors d are 5-deficient numbers (having sigma(d) < 5d).

%I A307115 #15 Apr 29 2019 20:59:54
%S A307115 122522400,147026880,183783600,205405200,220540320,232792560,
%T A307115 273873600,328648320,428828400,492972480,497296800,514594080,
%U A307115 537213600,563603040,575134560,581981400,605404800,627026400,629909280,670269600,684684000,710629920,739458720,745945200
%N A307115 Primitive 5-abundant numbers: Numbers k such that sigma(k) > 5k (A215264) all of whose proper divisors d are 5-deficient numbers (having sigma(d) < 5d).
%C A307115 Analogous to A071395 with abundancy index 5 instead of 2.
%C A307115 omega(a(n)) = A001221(a(n)) >= 6. - _David A. Corneth_, Mar 26 2019
%D A307115 Paul Erdős and János Surányi, Topics in the Theory of Numbers, New York: Springer, 2003, p. 243.
%H A307115 Amiram Eldar, <a href="/A307115/b307115.txt">Table of n, a(n) for n = 1..1000</a>
%H A307115 Graeme L. Cohen, <a href="https://doi.org/10.1090/S0025-5718-1984-0744936-X ">Primitive alpha-abundant numbers</a>, Mathematics of Computation, Vol. 43, No. 167 (1984), pp. 263-270.
%H A307115 Paul Erdős, <a href="https://users.renyi.hu/~p_erdos/1956-08.pdf">On additive arithmetical functions and applications of probability to number theory</a>, Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, Vol. 3 (1956), pp. 13-19.
%H A307115 Paul Erdős, <a href="http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-aav5i1p25bwm">Remarks on number theory. I: On primitive alpha-abundant numbers</a>, Acta Arithmetica., Vol. 5, No. 1 (1959), pp. 25-33, <a href="https://users.renyi.hu/~p_erdos/1959-20.pdf">alternative link</a>.
%t A307115 Select[Range@500000000, DivisorSigma[1, #] > 5 # && Times @@ Boole@ Map[DivisorSigma[1, #] < 5 # &, Most@ Divisors@ #] == 1 &] (* after _Michael De Vlieger_ at A071395 *)
%Y A307115 Cf. A000203, A001221, A071395, A215264.
%K A307115 nonn
%O A307115 1,1
%A A307115 _Amiram Eldar_, Mar 25 2019