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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS 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 Adjacent sequences:  A113902 A113903 A113904 * A113906 A113907 A113908 KEYWORD easy,nonn,changed AUTHOR Cino Hilliard, Jan 29 2006 STATUS approved

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Last modified August 18 10:34 EDT 2022. Contains 356212 sequences. (Running on oeis4.)