A336304 a(n) is the least number k such that the average number of prime divisors of {1..k} counted with multiplicity is >= n.

1, 4, 32, 2178, 416417176

Offset: 0

Author

Ilya Gutkovskiy, Nov 18 2020

Keywords

• nonn
• more

Examples

			a(1) = 4 since the average number of prime divisors of {1..4} counted with multiplicity equals (0 + 1 + 1 + 2)/4 = 1 which is >= 1 and this is the least such number.
a(3) = 2178 because the average number of prime divisors of {1..2178} counted with multiplicity is >= 3 and this is the least such number.
		

Links

• Eric Weisstein's World of Mathematics, Prime Factor.

Crossrefs

Cf. A001222, A022559, A085829, A328331, A338891, A338943.

Programs

Mathematica

s[n_] := Module[{m = 0, c = 0, k = 1, sum = 0, seq = {}}, While[c < n, sum += PrimeOmega[k]; If[sum >= m*k, c++; AppendTo[seq, k]; m++]; k++]; seq]; s[4] (* Amiram Eldar, Nov 18 2020 *)

PARI

a(n)=my(m=0,k=1);while(k>0, m+=bigomega(k); if(m>=k*n,break);k++);k \\ Derek Orr, Nov 18 2020