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A263821
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.
0
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
OFFSET
1,2
COMMENTS
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, ...
EXAMPLE
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.
MAPLE
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);
CROSSREFS
Cf. A000005.
Sequence in context: A333333 A376535 A095292 * A007293 A014596 A002823
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Oct 27 2015
STATUS
approved