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, 83860579775

Offset: 1

Author

Ilya Gutkovskiy, Nov 14 2020

Keywords

• nonn
• more
• changed

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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

Extensions

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

a(13) from Bill McEachen, Sep 01 2025