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

1,1

Links

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

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.

Example

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.

Crossrefs

In A007691 and A001599 but not in A003601.

Cf. A000005, A000203, A046985, A046987.

Sequence in context: A079598 A212302 A046999 * A330164 A323747 A028145

Adjacent sequences: A046983 A046984 A046985 * A046987 A046988 A046989

Keyword

nonn

Author

Labos Elemer

Extensions

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

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

Status

approved