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

1,2

Comments

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

Links

Table of n, a(n) for n=1..24.

Formula

Solution of the equation n’ = 3*n.

Example

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

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);

Crossrefs

Cf. A003415, A072873, A165558.

Sequence in context: A306059 A188785 A317237 * A188821 A181210 A092211

Adjacent sequences: A282768 A282769 A282770 * A282772 A282773 A282774

Keyword

nonn

Author

Paolo P. Lava, Mar 02 2017

Status

approved