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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