A181806 Positive integers with more highly composite divisors (A002182) than any smaller positive integer.

1, 2, 4, 12, 24, 48, 120, 240, 360, 720, 5040, 10080, 15120, 30240, 60480, 151200, 166320, 332640, 665280, 1663200, 1995840, 3326400, 8648640, 17297280, 21621600, 43243200, 86486400, 129729600, 259459200, 735134400

Offset

1,2

Comments

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.

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.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..153

A. Flammenkamp, List of the first 1200 highly composite numbers

Eric Weisstein's World of Mathematics, Highly composite number

Example

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.

Crossrefs

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

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

Includes all members of A136253.

Sequence in context: A089888 A291779 A181809 * A301416 A340137 A348092

Adjacent sequences: A181803 A181804 A181805 * A181807 A181808 A181809

Keyword

nonn

Author

Matthew Vandermast, Nov 27 2010

Extensions

a(20)-a(30) from Charles R Greathouse IV, Jan 14 2011

Status

approved