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Numbers n such that Omega(n) = Omega(n - Omega(n)), where Omega = A001222.
2

%I #17 Sep 18 2015 04:29:22

%S 1,3,6,30,35,40,45,51,57,60,66,78,87,88,93,95,102,104,105,117,121,123,

%T 136,140,143,145,156,161,174,175,185,187,203,205,215,217,219,221,232,

%U 237,245,249,258,261,267,282,285,289,291,301,303,305,321,323,325,329

%N Numbers n such that Omega(n) = Omega(n - Omega(n)), where Omega = A001222.

%C Omega=A001222: Number of prime divisors counted with multiplicity.

%C A198327 is a subsequence because, if n and n-2 are semiprimes, Omega(n) = 2, and n - 2 is semiprime, therefore Omega(n-2) = 2.

%H Vincenzo Librandi, <a href="/A200925/b200925.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5) = 35 because Omega(35) = 2 and Omega(35 - 2) = Omega(33) = 2.

%p with(numtheory):

%p isA200925 := proc(n)

%p bigomega(n-bigomega(n)) = bigomega(n) ;

%p end proc:

%p for n from 1 to 400 do

%p if isA200925(n) then printf("%d,",n) ; end if;

%p end do: # _R. J. Mathar_, Nov 282 2011

%t Select[Range[329], PrimeOmega[#] == PrimeOmega[# - PrimeOmega[#]] &] (* _T. D. Noe_, Nov 29 2011 *)

%Y Cf. A001222.

%K nonn

%O 1,2

%A _Michel Lagneau_, Nov 24 2011