A181809 Numbers n such that both n and n/2 are highly composite (A002182).

2, 4, 12, 24, 48, 120, 240, 360, 720, 1680, 2520, 5040, 10080, 15120, 20160, 50400, 55440, 110880, 166320, 221760, 332640, 554400, 665280, 1441440, 2162160, 2882880, 4324320, 7207200, 8648640, 14414400, 17297280, 21621600, 43243200, 73513440

Offset

1,1

Comments

These are the numbers that set records both for total number of divisors and for number of even divisors; intersection of A002182 and A181808.

For all positive integer values (j,k) such that jk = n, the number of divisors of n that are multiples of j equals A000005(k). Therefore, n sets a record for the number of its divisors that are multiples of j iff k=n/j is highly composite (A002182).

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Highly composite number

Example

The number 12 is both highly composite (A002182(5) = 12) and twice another highly composite number (12 = 2*6 = 2*A002182(4)).  It therefore has more divisors (A002183(5)=6) than any smaller positive integer, and more even divisors (A002183(4)=4) than any smaller positive integer. Since 12 is the third positive integer with the properties that define this sequence, a(3)=12.

Crossrefs

Numbers n such that 1 and 2 both appear in row n of A181803. See also A181808, A181810.

A053624 gives numbers that set records for number of odd divisors. No number sets records both for its number of odd divisors and its number of even divisors. Only the number 1 sets a record for its number of odd divisors and its number of total divisors.

Subsequence of A025487.

Sequence in context: A079352 A089888 A291779 * A181806 A301416 A340137

Adjacent sequences: A181806 A181807 A181808 * A181810 A181811 A181812

Keyword

nonn

Author

Matthew Vandermast, Nov 27 2010

Status

approved