A215264 Numbers k such that sigma(k) > 5*k.

122522400, 147026880, 183783600, 205405200, 220540320, 232792560, 245044800, 273873600, 294053760, 328648320, 367567200, 410810400, 428828400, 441080640, 465585120, 490089600, 492972480, 497296800, 514594080, 537213600, 547747200, 551350800, 563603040

Offset: 1

Author

Donovan Johnson, Aug 07 2012

Keywords

• nonn

Comments

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

Examples

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

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000
• Richard Laatsch, Measuring the Abundancy of Integers, Mathematics Magazine, Vol. 59, No. 2 (1986), pp. 84-92, alternative link.
• Gordon L. Miller and Mary T. Whalen, Multiply Abundant Numbers, School Science and Mathematics, Volume 95, Issue 5 (May 1995), pp. 256-259.
• Charles R. Wall, Phillip L. Crews and Donald B. Johnson, Density Bounds for the Sum of Divisors Function, Mathematics of Computation, Vol. 26, No. 119 (1972), pp. 773-777; Errata, Vol. 31, No. 138 (1977), p. 616.

Crossrefs

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

Programs

PARI

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

Formula

A001221(a(n)) >= 6 (Laatsch, 1986). - Amiram Eldar, Nov 07 2020