A239479 Integer solutions of the arithmetic differential equation m' = m - sqrt(m).

1, 9, 441, 815409, 553613841

Offset

1,2

Comments

a(6) > 10^17. - Giovanni Resta, Mar 20 2014

m = k^2, where k satisfies k' = (k-1)/2. - Charlie Neder, Mar 08 2019

Links

Table of n, a(n) for n=1..5.

Example

For m = 441 we have that m' = 420, sqrt(441) = 21 and 420 = 441 - 21.

Maple

with(numtheory); P:= proc(q) local n, p, x;
for n from 1 to q do x:=n^2;
if x*add(op(2, p)/op(1, p), p=ifactors(x)[2])=n^2-n then print(n^2);
fi; od; end: P(10^9);

Crossrefs

Cf. A003415, A239478.

Sequence in context: A167720 A287102 A173954 * A229625 A196965 A069073

Adjacent sequences: A239476 A239477 A239478 * A239480 A239481 A239482

Keyword

nonn,more

Author

Paolo P. Lava, Mar 20 2014

Status

approved