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A287238
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Numbers whose sum of proper divisors is equal to 95186291194.
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7
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118315669766, 130863307526, 181448867234, 184661404346, 184881064994, 185180602238, 186803095538, 187013065238, 187127594162, 187516992482, 187889460398, 188332874498, 188587837538, 188750086706, 189131019338, 189322730354, 189374121386, 189621107138
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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fini,full,nonn
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AUTHOR
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STATUS
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approved
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