OFFSET
1,2
COMMENTS
Also, largest number k such that, for each integer j from 1 to k, more multiples of j appear among the divisors of A002182(n) than appear among the divisors of any smaller positive integer.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
A. Flammenkamp, List of the first 1200 highly composite numbers
Eric Weisstein's World of Mathematics, Highly composite number
EXAMPLE
360 is a member of A002182, twice a member of A002182 (360/2 = 180), and three times a member of A002182 (360/3 = 120), but is not four times a member of A002182 (360/4 = 90 is not a member of A002182). Since A002182(13) = 360, a(13) = 3.
360 also sets records for the number of its divisors, the number of its divisors that are multiples of 2 (cf. A181808), and the number of its divisors that are multiples of 3, but not the number of its divisors that are multiples of 4.
MATHEMATICA
f[hc_, n_] := Module[{k=1}, While[MemberQ[hc, n/k], k++]; k-1]; s={}; hc={}; dm = 0; Do[d = DivisorSigma[0, n]; If[d > dm, dm = d; AppendTo[hc, n]]; AppendTo[s, f[hc, n]], {n, 1, 10^5}]; s (* Amiram Eldar, Jul 08 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Matthew Vandermast, Nov 27 2010
EXTENSIONS
a(5) corrected and more terms added by Amiram Eldar, Jul 08 2019
STATUS
approved