A338891 - OEIS

%I #19 Nov 18 2020 10:27:41

%S 1,21,165,1274,9435,69720,515230,3807265,28132035,207869515,

%T 1535959665,11349295155

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OddDivisorFunction.html">Odd Divisor Function</a>.

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

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

%t 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 *)

%o (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

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

%K nonn,more

%O 1,2

%A _Ilya Gutkovskiy_, Nov 14 2020

%E a(11)-a(12) from _Amiram Eldar_, Nov 16 2020