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%I #7 Aug 07 2022 15:47:06
%S 1,1,1,4,16,243,2187,65536,4194304,67108864,1073741824,152587890625,
%T 19073486328125,3656158440062976,131621703842267136,
%U 4738381338321616896,6140942214464815497216,3219905755813179726837607
%N omega(n!) raised to the power of bigomega(n!).
%C Sum of reciprocals converge to 3.317087986755007857557474300.. I found getting the 3 starting 1's interesting. 6 sequences begin with 1,1,1,4,16 and none begin with omegafactpowbigomegafact(n) = 1,1,1,4,16,243.
%F omega(x): number of distinct prime divisors of x. bigomega(x): number of prime divisors of x, counted with multiplicity.
%F a(n) = A000720(n)^A022559(n). - _Reinhard Zumkeller_, Feb 01 2006
%t Join[{1,1},PrimeNu[#]^PrimeOmega[#]&/@(Range[2,20]!)] (* _Harvey P. Dale_, Aug 07 2022 *)
%o (PARI) omegafactpowbigomegafact(n) = { local(x,a,b,s); s=0; for(x=0,n, a=omega(x!); b=bigomega(x!); s+=1./a^b; print1(a^b","); ); print(); print(s) }
%K easy,nonn
%O 0,4
%A _Cino Hilliard_, Jan 29 2006
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