A065127 Nonsquares with number of prime factors equal to twice the number of distinct prime factors.
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
Examples
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.
Links
- Harry J. Smith, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
Select[Range[1000],!IntegerQ[Sqrt[#]]&&PrimeOmega[#]==2*PrimeNu[#]&] (* Harvey P. Dale, Jul 05 2023 *)
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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
Formula
n = prod( p(i)^e(i)) i in [1, k] => sum( e(i)), i in [1, k] == 2k
Extensions
OFFSET changed from 0 to 1 by Harry J. Smith, Oct 11 2009
Comments