login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A338891
a(n) is the least number k such that the average number of odd divisors of {1..k} is >= n.
5
1, 21, 165, 1274, 9435, 69720, 515230, 3807265, 28132035, 207869515, 1535959665, 11349295155
OFFSET
1,2
LINKS
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
KEYWORD
nonn,more
AUTHOR
Ilya Gutkovskiy, Nov 14 2020
EXTENSIONS
a(11)-a(12) from Amiram Eldar, Nov 16 2020
STATUS
approved