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A065127
Nonsquares with number of prime factors equal to twice the number of distinct prime factors.
2
24, 40, 54, 56, 88, 104, 135, 136, 152, 184, 189, 232, 240, 248, 250, 296, 297, 328, 336, 344, 351, 360, 375, 376, 424, 459, 472, 488, 504, 513, 528, 536, 540, 560, 568, 584, 600, 621, 624, 632, 664, 686, 712, 756, 776, 783, 792, 808, 810, 816, 824, 837
OFFSET
1,1
COMMENTS
Close to A065036 but not the same. One of several quasi-square classes.
LINKS
FORMULA
n = prod( p(i)^e(i)) i in [1, k] => sum( e(i)), i in [1, k] == 2k
EXAMPLE
240=2^4*3*5 so there are 3 distinct prime factors, sum of exponents is 6=2*3 and 240 is not a square so is in the list.
MATHEMATICA
Select[Range[1000], !IntegerQ[Sqrt[#]]&&PrimeOmega[#]==2*PrimeNu[#]&] (* Harvey P. Dale, Jul 05 2023 *)
PROG
(PARI) n=0; for (m=1, 10^9, if (issquare(m), next); if (bigomega(m) == 2*omega(m), write("b065127.txt", n++, " ", m); if (n==1000, return))) \\ Harry J. Smith, Oct 12 2009
(PARI) is(n)=my(f=factor(n)); issquare(n) && bigomega(f)==2*omega(f) \\ Charles R Greathouse IV, Oct 15 2015; corrected by Michel Marcus, Apr 25 2020
CROSSREFS
Sequence in context: A360793 A375076 A297401 * A065036 A329880 A303359
KEYWORD
easy,nonn
AUTHOR
Olivier Gérard, Nov 14 2001
EXTENSIONS
OFFSET changed from 0 to 1 by Harry J. Smith, Oct 11 2009
STATUS
approved