A181808 Numbers that set a record for number of even divisors: a(n) = 2*A002182(n).

2, 4, 8, 12, 24, 48, 72, 96, 120, 240, 360, 480, 720, 1440, 1680, 2520, 3360, 5040, 10080, 15120, 20160, 30240, 40320, 50400, 55440, 90720, 100800, 110880, 166320, 221760, 332640, 443520, 554400, 665280, 997920, 1108800, 1330560, 1441440, 2162160, 2882880, 4324320

Offset: 1

Author

Matthew Vandermast, Nov 27 2010

Keywords

• nonn

Comments

In other words, a positive integer n appears in the sequence iff more even numbers divide n than divide any positive integer smaller than n.

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). Cf. A181803, A181809, A181810.

Examples

			a(4)=12 has exactly four even divisors (2, 4, 6 and 12).  (Note that these are precisely the numbers that are twice a divisor of A002182(4)=6; see row 6 of A027750.)  No positive integer smaller than 12 has as many as four even divisors; hence, 12 is a member of the sequence.
		

Links

• Eric Weisstein's World of Mathematics, Highly composite number

Crossrefs

Numbers n such that 2 appears in row n of A181803. See also A181809, A181810.

A002183(n) gives number of even divisors of a(n).

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.

Formula

a(n)=2*A002182(n).