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A336304 a(n) is the least number k such that the average number of prime divisors of {1..k} counted with multiplicity is >= n. 3
1, 4, 32, 2178, 416417176 (list; graph; refs; listen; history; text; internal format)
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: A257583 A258122 A012092 * A027639 A117620 A347484

Adjacent sequences:  A336301 A336302 A336303 * A336305 A336306 A336307

KEYWORD

nonn,more

AUTHOR

Ilya Gutkovskiy, Nov 18 2020

STATUS

approved

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Last modified January 22 00:08 EST 2022. Contains 350481 sequences. (Running on oeis4.)