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

0,2

Links

Table of n, a(n) for n=0..4.

Eric Weisstein's World of Mathematics, Prime Factor.

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A258122 A012092 A367530 * A027639 A117620 A347484

Adjacent sequences: A336301 A336302 A336303 * A336305 A336306 A336307

Keyword

nonn,more

Author

Ilya Gutkovskiy, Nov 18 2020

Status

approved