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A263821
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Numbers x such that x = Sum_{j=0..k}{d(x)^j}, for some k, where d(x) is the number of divisors of x.
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0
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1, 3, 4, 9, 14, 25, 49, 50, 55, 91, 121, 135, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2072, 2209, 2388, 2809, 3481, 3721, 4489, 5041, 5329, 5664, 6421, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12056, 12769, 16129, 16952, 17161, 18769, 19321, 22201, 22801
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OFFSET
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1,2
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COMMENTS
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Values of k are 0, 1, 1, 2, 2, 4, 6, 3, 4, 5, 10, 4, 12, 16, 18, 22, 28, 30, 36, 40, 42, 6, 46, 7, 52, 58, 60, 66, 70, 72, 7, 78, 82, 88, 96, 100, 102, 106, 108, 10, 112, 126, 11, 130, 136, 138, 148, 150, ...
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LINKS
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EXAMPLE
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d(25^0) + d(25^1) + d(25^2) +d(25^3) + d(25^4) = 1 + 3 + 5 + 7 + 9 = 25;
d(91^0) + d(91^1) + d(91^2) + d(91^3) + d(91^4) + d(91^5) = 1 + 4 + 9 + 16 + 25 + 36 = 91;
d(2072^0) + d(2072^1) + d(2072^2) + d(2072^3) + d(2072^4) + d(2072^5) + d(2072^6) = 1 + 16 + 63 + 160 + 325 + 576 + 931 = 2072.
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MAPLE
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with(numtheory): P:= proc(q) local a, k, n;
for n from 1 to q do a:=0; k:=-1;
while a<n do k:=k+1; a:=a+tau(n^k); od;
if a=n then print(n); fi; od; end: P(10^9);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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