A046999 Numbers k whose average divisor is nonintegral and divides k.

28, 496, 8128, 950976, 2178540, 33550336, 142990848, 301953024, 459818240, 675347400, 714954240, 995248800, 1379454720, 2701389600, 3288789504, 6720569856, 8589869056, 10200236032, 14254365440, 30600708096, 42763096320, 43861478400, 66433720320, 71271827200

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

The sequence contains perfect numbers (A000396) and others. Most of them have only small prime factors.

The first three terms are in A007691 (multiply perfect numbers) but 950976 is not since sigma_1/k is not an integer.

sigma_0(k) is the number of divisors of k (A000005).

sigma_1(k) is the sum of the divisors of k [same as sigma(k)] (A000203).

Harmonic numbers that are not arithmetic numbers. Of the 937 harmonic numbers below 10^14 there are just 90 such terms, of them 13 are multiply perfect numbers. - Amiram Eldar, Jun 08 2020

Examples

			k=28, sigma_0=6, sigma_1=56, m=sigma_1/sigma_0=9.333... is not an integer, but k/m=3 is;
k=950976, m=2958592/84=3521.333... but k/m=27 is integral.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..90 (terms below 10^14)

Crossrefs

In A001599 but not in A003601.

Cf. A007691, A046985, A046986, A046987, A000396.

Formula

Average divisor = m = sigma_1(k)/sigma_0(k) is not an integer but k/m is.

Extensions

More terms from Jud McCranie, Dec 25 2000

a(16)-a(24) from Donovan Johnson, Apr 22 2008