|
|
A210935
|
|
Numbers n for which n*n'/(n+n') is an integer, where n' is the arithmetic derivative of n.
|
|
1
|
|
|
1, 4, 64, 80, 108, 270, 351, 432, 729, 768, 864, 2916, 5184, 5832, 6250, 6912, 12096, 13500, 16384, 25600, 32832, 34992, 37500, 39366, 43200, 46656, 50000, 73008, 74304, 81648, 84375, 110592, 131250, 138240, 143748, 153664, 172800, 176418, 200000, 225000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Only eleven odd numbers in the first 150 terms: a(1)=1, a(7)=351, a(9)=729, a(31)=84375, a(76)=2470629, a(78)=2709375, a(87)=4159375, a(89)=4348377, a(115)=13286025, a(126)=22235661, a(128)=25059375.
|
|
LINKS
|
|
|
EXAMPLE
|
n=729; n'=1458; n*n'/(n+n')=486.
|
|
MAPLE
|
with(numtheory);
local a, i, p, pfs;
for i from 1 to n do
pfs:=ifactors(i)[2]; a:=i*add(op(2, p)/op(1, p), p=pfs) ;
if a*i/(a+i)=trunc(a*i/(a+i)) then print(i); fi;
od; end:
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|