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

1,1

Comments

Close to A065036 but not the same. One of several quasi-square classes.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

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: A362594 A360793 A297401 * A065036 A329880 A303359

Adjacent sequences: A065124 A065125 A065126 * A065128 A065129 A065130

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