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.

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, ...

Links

Table of n, a(n) for n=1..48.

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: A207016 A333333 A095292 * A007293 A014596 A002823

Adjacent sequences: A263818 A263819 A263820 * A263822 A263823 A263824

Keyword

nonn

Author

Paolo P. Lava, Oct 27 2015

Status

approved