A067801 Numbers m such that bigomega(m)=2*omega(m).

1, 4, 9, 24, 25, 36, 40, 49, 54, 56, 88, 100, 104, 121, 135, 136, 152, 169, 184, 189, 196, 225, 232, 240, 248, 250, 289, 296, 297, 328, 336, 344, 351, 360, 361, 375, 376, 424, 441, 459, 472, 484, 488, 504, 513, 528, 529, 536, 540, 560, 568, 584, 600, 621, 624

Offset: 1

Author

Benoit Cloitre, Feb 07 2002

Keywords

• nonn

Comments

There are A000041(k) distinct prime signatures of length k. - David A. Corneth, Apr 25 2020

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

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000041, A001221, A001222.

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

Programs

Mathematica

Select[Range[700], PrimeOmega[#] == 2*PrimeNu[#] &] (* Jean-François Alcover, Jun 29 2013 *)

PARI

is(n)=my(f=factor(n)[,2]); vecsum(f)==2*#f \\ Charles R Greathouse IV, Oct 15 2015

Formula

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