A287238 Numbers whose sum of proper divisors is equal to 95186291194.

118315669766, 130863307526, 181448867234, 184661404346, 184881064994, 185180602238, 186803095538, 187013065238, 187127594162, 187516992482, 187889460398, 188332874498, 188587837538, 188750086706, 189131019338, 189322730354, 189374121386, 189621107138

Offset

1,1

Comments

The number 95186291194 is the 46th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.

There are exactly 112 elements in the sequence.

In 2016, C. Pomerance proved that, for every e>0, the number of preimages is O_e(n^{2/3+e}).

Conjecture: there exists a positive real number k > 1 such that the number of preimages of an even number n is O((log n)^k).

Links

Anton Mosunov, Table of n, a(n) for n = 1..112

C. Pomerance, The first function and its iterates, A Celebration of the Work of R. L. Graham, S. Butler, J. Cooper, and G. Hurlbert, eds., Cambridge U. Press, to appear.

Example

a(1) = 118315669766, because it is the smallest number whose sum of proper divisors is equal to 95186291194: 1 + 2 + 7 + 14 + 19 + 38 + 133 + 266 + 444795751 + 889591502 + 3113570257 + 6227140514 + 8451119269 + 16902238538 + 59157834883 = 95186291194.

Crossrefs

Cf. A001065, A283156, A283157, A287233, A287247, A287251, A287262.

Sequence in context: A288275 A287233 A122717 * A072718 A034652 A015402

Adjacent sequences: A287235 A287236 A287237 * A287239 A287240 A287241

Keyword

fini,full,nonn

Author

Anton Mosunov, May 22 2017

Status

approved