A239478 Integer solutions of the arithmetic differential equation m' = m + sqrt(m).

225, 184041, 741321, 1095543801, 1225901036420447409, 149122302188995046961, 46817968644647134406949912561, 54295775728226475449655917952369, 75857110437235916587904557376695281, 14908043822211741703982271584015636203475818689847929

Offset

1,1

Comments

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

It follows that 2k is a Giuga number satisfying (2k)' = 2k + 1. - Max Alekseyev, Sep 09 2025

Links

Table of n, a(n) for n=1..10.

Formula

For n <= 12, a(n) = (A007850(n)/2)^2. - Max Alekseyev, Sep 09 2025

Example

For m = 225 we have that m' = 240, sqrt(225) = 15 and 240 = 225 + 15.

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, A007850, A239479.

Sequence in context: A260864 A265420 A171109 * A304314 A109688 A195277

Adjacent sequences: A239475 A239476 A239477 * A239479 A239480 A239481

Keyword

nonn

Author

Paolo P. Lava, Mar 20 2014

Extensions

Terms a(5) onward from Max Alekseyev, Sep 09 2025

Status

approved