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A282771 Integers that are one third of their arithmetic derivatives. 0

%I #9 Mar 02 2017 03:40:22

%S 0,64,432,2916,19683,50000,337500,2278125,13176688,39062500,88942644,

%T 263671875,600362847,10294287500,30517578125,69486440625,

%U 2712892291396,4564986729776,8042412109375,18312022966923,30813660425988,207992207875419,2119447102653125,3566395882637500

%N Integers that are one third of their arithmetic derivatives.

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

%F Solution of the equation nā€™ = 3*n.

%e 337500 = 2^2*3^3*5^5, 337500ā€™ = 1012500 and 337500 = 3*1012500.

%p with(numtheory): with(combinat): P:=proc(q) local a,k,n,x,y;

%p 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;

%p 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);

%p for k from 1 to 100 do print(y[k]); od; end: P(10);

%Y Cf. A003415, A072873, A165558.

%K nonn

%O 1,2

%A _Paolo P. Lava_, Mar 02 2017

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Last modified June 23 08:04 EDT 2024. Contains 373629 sequences. (Running on oeis4.)