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A282771 Integers that are one third of their arithmetic derivatives. 0
0, 64, 432, 2916, 19683, 50000, 337500, 2278125, 13176688, 39062500, 88942644, 263671875, 600362847, 10294287500, 30517578125, 69486440625, 2712892291396, 4564986729776, 8042412109375, 18312022966923, 30813660425988, 207992207875419, 2119447102653125, 3566395882637500 (list; graph; refs; listen; history; text; internal format)
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 nā€™ = 3*n.

EXAMPLE

337500 = 2^2*3^3*5^5,  337500ā€™ = 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

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Last modified October 22 16:15 EDT 2021. Contains 348174 sequences. (Running on oeis4.)