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A145193 Omega(6n-1) + Omega(6n+1). 3

%I #8 Sep 04 2013 12:58:00

%S 2,2,2,3,2,3,2,3,3,2,3,2,3,3,3,3,2,2,3,4,4,3,2,4,2,3,3,3,4,2,4,2,2,4,

%T 3,4,3,2,3,2,5,3,3,3,2,4,2,4,3,4,3,2,3,5,3,3,5,2,3,3,3,3,3,4,3,3,3,3,

%U 4,2,5,2,3,3,3,4,2,3,5,3,3,3,3,3,3

%N Omega(6n-1) + Omega(6n+1).

%H Charles R Greathouse IV, <a href="/A145193/b145193.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A001222(6n-1) + A001222(6n+1). - _Michel Marcus_, Sep 04 2013

%e For n=1, Omega(6n-1) + Omega(6n+1) = Omega(5) + Omega(7) = 1+1 = 2, so a(1)=2.

%t For[x=6, x<601, x+=6,S=0;T=0;For[k=1, k< Length[FactorInteger[x-1]]+1,k++,S+= FactorInteger[x-1][[k]][[2]]];For[m=1, m<Length[FactorInteger[x+1]]+1,m++,T+= FactorInteger[x+1][[m]][[2]]]; Print[x/6," ",S+T]]

%t Table[Total[PrimeOmega/@(6n+{1,-1})],{n,60}] (* _Harvey P. Dale_, May 22 2013 *)

%o (PARI) a(n) = bigomega(6*n-1) + bigomega(6*n+1); \\ _Michel Marcus_, Sep 04 2013

%Y Cf. A145194.

%K nonn,easy

%O 1,1

%A _Arran Fernandez_, Oct 03 2008

%E More terms from _Michel Marcus_, Sep 04 2013

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)