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A072588 Numbers having at least one prime factor with an odd and one with an even exponent. 2
12, 18, 20, 28, 44, 45, 48, 50, 52, 60, 63, 68, 72, 75, 76, 80, 84, 90, 92, 98, 99, 108, 112, 116, 117, 124, 126, 132, 140, 147, 148, 150, 153, 156, 162, 164, 171, 172, 175, 176, 180, 188, 192, 198, 200, 204, 207, 208, 212, 220, 228, 234, 236, 240, 242, 244 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

= Complement(Union(A002035, A000290)) = Intersection(A000037, A072587);

a(k)=A070011(k) for 0<k<=25, A070011(26)=120 is not a term, as 120=5*3*2^3 having only odd exponents (A002035(85)=120),

and a(54)=240 is not a term of A070011, as from 240=5*3*2^4 follows that A001222(240)/A001221(240)=6/3=2 is an integer.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

MATHEMATICA

oeeQ[n_]:=Module[{fi=Transpose[FactorInteger[n]][[2]]}, Count[fi, _?OddQ]>0  && Count[fi, _?EvenQ]>0]; Select[Range[250], oeeQ] (* Harvey P. Dale, Jun 21 2015 *)

PROG

(Haskell)

a072588 n = a072588_list !! (n-1)

a072588_list = filter f [1..] where

   f x = any odd es && any even es  where es = a124010_row x

-- Reinhard Zumkeller, Nov 15 2012

(PARI) is(n)=#Set(factor(n)[, 2]%2)==2 \\ Charles R Greathouse IV, Oct 16 2015

CROSSREFS

Cf. A124010.

Sequence in context: A162947 A070011 A084679 * A267117 A187039 A325241

Adjacent sequences:  A072585 A072586 A072587 * A072589 A072590 A072591

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jun 23 2002

STATUS

approved

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Last modified July 12 22:46 EDT 2020. Contains 335669 sequences. (Running on oeis4.)