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A088533
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Numbers n such that Bigomega(n!)/Omega(n!) is an integer.
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2
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2, 3, 4, 7, 15, 22, 24, 40, 49, 58, 71, 74, 92, 124, 179, 183, 232, 237, 413, 542, 547, 731, 752, 758, 983, 1266, 1283, 1289, 1336, 1706, 1712, 1725, 2656, 2909, 3509, 3612, 3653, 3674, 3702, 3709, 4617, 4646, 4697, 5993
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OFFSET
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1,1
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LINKS
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FORMULA
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Let k = number of prime divisors of n! counted with multiplicity; b = number of distinct prime divisors of n!. Then n is in sequence if k/b is an integer.
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EXAMPLE
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S(4!) = bigomega(4!) / omega(4!) = 4/2 = 2 so 4 is 3rd term in the sequence.
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MATHEMATICA
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ointQ[n_]:=Module[{f=n!}, IntegerQ[PrimeOmega[f]/PrimeNu[f]]]; Select[Range[ 2, 6000], ointQ] (* Harvey P. Dale, Dec 07 2013 *)
Omega = Nu = 0; a = {}; Do[If[PrimeQ[n], Nu++]; Omega += PrimeOmega[n];
If[Divisible[Omega, Nu], AppendTo[a, n]], {n, 2, 6000}]; a (* Ivan Neretin, Mar 14 2017 *)
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PROG
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(PARI) for(x=2, 10000, x1=x!; y=bigomega(x1)/omega(x1); if(y==floor(y), print1((x)", ")))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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