A338891 a(n) is the least number k such that the average number of odd divisors of {1..k} is >= n.

1, 21, 165, 1274, 9435, 69720, 515230, 3807265, 28132035, 207869515, 1535959665, 11349295155

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Eric Weisstein's World of Mathematics, Odd Divisor Function.

Formula

a(n+1)/a(n) approaches e^2.

Example

a(5) = 9435 because the average number of odd divisors of {1..9435} is >= 5.

Mathematica

m = 1; sum = 0; s = {}; Do[sum += DivisorSigma[0, k/2^IntegerExponent[k, 2]]; If[sum >= m*k, AppendTo[s, k]; m++], {k, 1, 10^6}]; s (* Amiram Eldar, Nov 15 2020 *)

Prog

(PARI) a(n) = my(s=1, k=1); while(s<k*n, k++; s=s+numdiv(k>>valuation(k, 2))); k; \\ Michel Marcus, Nov 14 2020

Crossrefs

Cf. A001227, A060831, A072334, A085829, A328331, A338943.

Sequence in context: A070315 A242191 A146301 * A126993 A332944 A022681

Adjacent sequences: A338888 A338889 A338890 * A338892 A338893 A338894

Keyword

nonn,more

Author

Ilya Gutkovskiy, Nov 14 2020

Extensions

a(11)-a(12) from Amiram Eldar, Nov 16 2020

Status

approved