A210935 Numbers n for which n*n'/(n+n') is an integer, where n' is the arithmetic derivative of n.

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

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

Paolo P. Lava and Donovan Johnson, Table of n, a(n) for n = 1..500 (first 150 terms from Paolo P. Lava)

Example

n=729; n'=1458; n*n'/(n+n')=486.

Maple

with(numtheory);
A210935:= proc(n)
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:
A210935(100000000);

Crossrefs

Cf. A003415, A165562.

Sequence in context: A368111 A367913 A381270 * A090561 A273375 A016934

Adjacent sequences: A210932 A210933 A210934 * A210936 A210937 A210938

Keyword

nonn

Author

Paolo P. Lava, May 11 2012

Status

approved