A046986 Multiply perfect numbers that are also harmonic numbers but are not arithmetic numbers.

28, 496, 8128, 2178540, 33550336, 142990848, 459818240, 1379454720, 8589869056, 43861478400, 66433720320, 137438691328, 704575228896, 181742883469056, 6088728021160320, 14942123276641920, 20158185857531904, 275502900594021408, 622286506811515392, 2305843008139952128

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			k = 2178540 is a term since s0 = d(k) = 216 and s1 = sigma(k) = 8714160, s1/s0 = 8714160/216 = 121030/3 is not an integer, and (k * s0)/s1 = (2178540 * 216)/8714160 = 54 and s1/k = 8714160/2178540 = 4 are integers.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..207

Crossrefs

In A007691 and A001599 but not in A003601.

Cf. A000005, A000203, A046985, A046987.

Formula

Let s1 be the sum of divisors of k and s0 be the number of divisors of k. Then, k is a term if k | s1, s1 | (k * s0), but s1 is not divisible by s0.

Extensions

a(12)-a(17) from Donovan Johnson, Nov 30 2008

Edited and a(18)-a(21) added by Amiram Eldar, May 09 2024