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

Author

Anton Mosunov, May 22 2017

Keywords

• fini
• full
• nonn

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).

Examples

			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.
		

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.

Crossrefs

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