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A317102 Powerful numbers whose distinct prime multiplicities are pairwise indivisible. 8
1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 169, 196, 200, 216, 225, 243, 256, 288, 289, 343, 361, 392, 432, 441, 484, 500, 512, 529, 625, 648, 675, 676, 729, 800, 841, 864, 900, 961, 968, 972, 1000, 1024, 1089, 1125, 1152, 1156, 1225 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A number is powerful if its prime multiplicities are all greater than 1.

LINKS

Robert Israel, Table of n, a(n) for n = 1..3000

EXAMPLE

144 = 2^4 * 3^2 is not in the sequence because 4 and 2 are not pairwise indivisible.

MAPLE

filter:= proc(n) local L, i, j, q;

  L:= convert(map(t -> t[2], ifactors(n)[2]), set);

  if min(L) = 1 then return false fi;

  for j from 2 to nops(L) do

    for i from 1 to j-1 do

      q:= L[i]/L[j];

      if q::integer or (1/q)::integer then return false fi;

  od od;

  true

end proc:

select(filter, [$4..10000]); # Robert Israel, Jun 23 2019

MATHEMATICA

Select[Range[1000], And[Max@@Last/@FactorInteger[#]>=2, Select[Tuples[Last/@FactorInteger[#], 2], And[UnsameQ@@#, Divisible@@#]&]=={}]&]

CROSSREFS

Cf. A001694, A056239, A112798, A118914, A124010, A285572, A285573, A303362, A304713, A316475, A317101, A317616.

Sequence in context: A158804 A080366 A001694 * A157985 A001597 A072777

Adjacent sequences:  A317099 A317100 A317101 * A317103 A317104 A317105

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 01 2018

EXTENSIONS

Definition corrected and a(1)=1 inserted by Robert Israel, Jun 23 2019

STATUS

approved

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Last modified September 27 13:39 EDT 2020. Contains 337380 sequences. (Running on oeis4.)