A067801 - OEIS

%I #43 Apr 24 2022 07:40:19

%S 1,4,9,24,25,36,40,49,54,56,88,100,104,121,135,136,152,169,184,189,

%T 196,225,232,240,248,250,289,296,297,328,336,344,351,360,361,375,376,

%U 424,441,459,472,484,488,504,513,528,529,536,540,560,568,584,600,621,624

%N Numbers m such that bigomega(m)=2*omega(m).

%C There are A000041(k) distinct prime signatures of length k. - _David A. Corneth_, Apr 25 2020

%C A square k is a term iff k belongs to A062503; in this case, k = p_1^2 * p_2^2 *...* p_r^2 and bigomega(k) = 2*omega(k) = 2*r. - _Bernard Schott_, Apr 25 2020

%H Enrique Pérez Herrero, <a href="/A067801/b067801.txt">Table of n, a(n) for n = 1..5000</a>

%F Numbers m such that A001222(m) = 2*A001221(m)

%t Select[Range[700], PrimeOmega[#] == 2*PrimeNu[#] &] (* _Jean-François Alcover_, Jun 29 2013 *)

%o (PARI) is(n)=my(f=factor(n)[,2]); vecsum(f)==2*#f \\ _Charles R Greathouse IV_, Oct 15 2015

%Y Cf. A000041, A001221, A001222.

%Y Cf. also A065127 (subsequence of nonsquares), A062503 (subsequence of squares).

%K nonn

%O 1,2

%A _Benoit Cloitre_, Feb 07 2002