A113905 omega(n!) raised to the power of bigomega(n!).

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.

Links

Table of n, a(n) for n=0..17.

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

Author

Cino Hilliard, Jan 29 2006

Status

approved