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Positive integers with more highly composite divisors (A002182) than any smaller positive integer.
8

%I #16 Oct 15 2024 04:23:30

%S 1,2,4,12,24,48,120,240,360,720,5040,10080,15120,30240,60480,151200,

%T 166320,332640,665280,1663200,1995840,3326400,8648640,17297280,

%U 21621600,43243200,86486400,129729600,259459200,735134400

%N Positive integers with more highly composite divisors (A002182) than any smaller positive integer.

%C Numbers n such that A181801(n) > A181801(m) for all m < n. Also, numbers n such that row n of triangles A181802 and A181803 is longer than any previous row in either triangle.

%C Not a subsequence of A002182. The smallest positive integer which has a record number of highly composite divisors, but which is not highly composite itself, is 30240.

%H Charles R Greathouse IV, <a href="/A181806/b181806.txt">Table of n, a(n) for n = 1..153</a>

%H A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.txt">List of the first 1200 highly composite numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly composite number</a>

%e 12 has five divisors (namely, 1, 2, 4, 6 and 12) that are members of A002182. No positive integer smaller than 12 has more than three members of A002182 among its divisors; hence, 12 is a member of the sequence.

%Y A181807(n) = number of highly composite divisors of a(n) (i.e., A181801(a(n))).

%Y Subsequence of A025487, A181804. Numbers A181804(n) such that A181805(n) increases to a record.

%Y Includes all members of A136253.

%K nonn

%O 1,2

%A _Matthew Vandermast_, Nov 27 2010

%E a(20)-a(30) from _Charles R Greathouse IV_, Jan 14 2011