A282771 Integers that are one third of their arithmetic derivatives.

0, 64, 432, 2916, 19683, 50000, 337500, 2278125, 13176688, 39062500, 88942644, 263671875, 600362847, 10294287500, 30517578125, 69486440625, 2712892291396, 4564986729776, 8042412109375, 18312022966923, 30813660425988, 207992207875419, 2119447102653125, 3566395882637500

Offset: 1

Author

Paolo P. Lava, Mar 02 2017

Keywords

• nonn

Comments

All integers of the form p^p*q^q*r^r, with p, q and r primes, are in the sequence.

Examples

			337500 = 2^2*3^3*5^5,  337500’ = 1012500 and 337500 = 3*1012500.
		

Crossrefs

Cf. A003415, A072873, A165558.

Programs

Maple

with(numtheory): with(combinat): P:=proc(q) local a,k,n,x,y;
x:=[]; y:=[]; for n from 1 to q do for k from 1 to 3 do x:=[op(x),ithprime(n)^ithprime(n)]; od; od;
a:=choose(x,3); for k from 1 to nops(a) do y:=[op(y),convert(a[k],`*`)]; od; y:=sort([op(y)]); print(0);
for k from 1 to 100 do print(y[k]); od; end: P(10);

Formula

Solution of the equation n’ = 3*n.