A215264 - OEIS

%I #30 Feb 13 2021 06:29:41

%S 122522400,147026880,183783600,205405200,220540320,232792560,

%T 245044800,273873600,294053760,328648320,367567200,410810400,

%U 428828400,441080640,465585120,490089600,492972480,497296800,514594080,537213600,547747200,551350800,563603040

%N Numbers k such that sigma(k) > 5*k.

%C The asymptotic density of this sequence is > 1/a(1) ~ 8*10^(-9). Wall et al. (1972) proved that it is < 0.0122. - _Amiram Eldar_, Feb 13 2021

%H Donovan Johnson, <a href="/A215264/b215264.txt">Table of n, a(n) for n = 1..10000</a>

%H Richard Laatsch, <a href="http://www.jstor.org/stable/2690424">Measuring the Abundancy of Integers</a>, Mathematics Magazine, Vol. 59, No. 2 (1986), pp. 84-92, <a href="https://isidore.co/misc/Physics%20papers%20and%20books/Zotero/storage/99C5C5IC/Laatsch%20-%201986%20-%20Measuring%20the%20Abundancy%20of%20Integers.pdf">alternative link</a>.

%H Gordon L. Miller and Mary T. Whalen, <a href="https://doi.org/10.1111/j.1949-8594.1995.tb15776.x">Multiply Abundant Numbers</a>, School Science and Mathematics, Volume 95, Issue 5 (May 1995), pp. 256-259.

%H Charles R. Wall, Phillip L. Crews and Donald B. Johnson, <a href="https://doi.org/10.1090/S0025-5718-1972-0327700-7">Density Bounds for the Sum of Divisors Function</a>, Mathematics of Computation, Vol. 26, No. 119 (1972), pp. 773-777; <a href="https://doi.org/10.1090/S0025-5718-1977-0427251-X">Errata</a>, Vol. 31, No. 138 (1977), p. 616.

%F A001221(a(n)) >= 6 (Laatsch, 1986). - _Amiram Eldar_, Nov 07 2020

%e sigma(122522400) = 614210688 and 614210688 > 5 * 122522400.

%o (PARI) for(n=122522400, 563603040, if(sigma(n)>5*n, print1(n ", ")))

%Y Cf. A000203, A001221, A023199, A068403, A068404.

%K nonn

%O 1,1

%A _Donovan Johnson_, Aug 07 2012