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A113905
omega(n!) raised to the power of bigomega(n!).
0
1, 1, 1, 4, 16, 243, 2187, 65536, 4194304, 67108864, 1073741824, 152587890625, 19073486328125, 3656158440062976, 131621703842267136, 4738381338321616896, 6140942214464815497216, 3219905755813179726837607
OFFSET
0,4
COMMENTS
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.
FORMULA
omega(x): number of distinct prime divisors of x. bigomega(x): number of prime divisors of x, counted with multiplicity.
a(n) = A000720(n)^A022559(n). - Reinhard Zumkeller, Feb 01 2006
MATHEMATICA
Join[{1, 1}, PrimeNu[#]^PrimeOmega[#]&/@(Range[2, 20]!)] (* Harvey P. Dale, Aug 07 2022 *)
PROG
(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) }
CROSSREFS
Sequence in context: A271267 A333438 A232840 * A200045 A099202 A139288
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Jan 29 2006
STATUS
approved