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A201009 Numbers n such that the set of distinct prime divisors of n is equal to the set of distinct prime divisors of the arithmetic derivative n'. 1
1, 4, 16, 27, 108, 144, 256, 432, 500, 784, 972, 1323, 1728, 2700, 2916, 3125, 3456, 5292, 8788, 11664, 12500, 13068, 15376, 16875, 19683, 20736, 23328, 25000, 27648, 28125, 31212, 34300, 47916, 54000, 57132, 65536, 72000, 78732, 97556, 102400, 103788, 104544 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A027748(n,k) = A027748(A003415(n),k) for k=1..A001221(n). - Reinhard Zumkeller, Jan 16 2013

A051674 is a subset of this sequence.

LINKS

Paolo P. Lava and Donovan Johnson, Table of n, a(n) for n = 1..500 (first 100 terms from Paolo P. Lava)

EXAMPLE

n = 1728 = 2^6*3^3, n' = 6912 = 2^8*3^3 have the same prime factors 2 and 3.

MAPLE

with(numtheory);

A201009:=proc(q)

local a, b, k, n;

for n from 1 to q do

  a:=ifactors(n)[2]; b:=ifactors(n*add(op(2, p)/op(1, p), p=ifactors(n)[2]))[2];

  if nops(a)=nops(b) then

    if product(a[k][1], k=1..nops(a))=product(b[k][1], k=1..nops(a)) then print(n);

fi; fi; od; end:

A201009(100000); # Paolo P. Lava, Jan 09 2013

PROG

(Haskell)

a201009 = a201009_list

a201009_list = 1 : filter

   (\x -> a027748_row x == a027748_row (a003415 x)) [2..]

-- Reinhard Zumkeller, Jan 16 2013

(Python)

from sympy import primefactors, factorint

A201009 = [n for n in range(1, 10**5) if primefactors(n) == primefactors(sum([int(n*e/p) for p, e in factorint(n).items()]) if n > 1 else 0)] # Chai Wah Wu, Aug 21 2014

CROSSREFS

Cf. A003415, A055744, A081377, A110751, A110819.

Sequence in context: A072873 A072653 A008478 * A111260 A067688 A097374

Adjacent sequences:  A201006 A201007 A201008 * A201010 A201011 A201012

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Jan 09 2013

STATUS

approved

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Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)