A353936 a(n) is the n-th highly composite number (A002182) divided by the smallest highly composite number with at least half as many divisors, or 0 if the quotient is not an integer.

2, 2, 3, 3, 4, 3, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 9, 8, 9, 8, 10, 11, 9, 10, 11, 11, 11, 11, 11, 11, 12, 11, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 15, 0, 16, 15, 15, 17, 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 19, 17, 18, 19, 19, 18, 19, 19, 19

Offset

2,1

Comments

This sequence has infinitely many prime terms and infinitely many composite terms.

Links

Table of n, a(n) for n=2..73.

Example

a(8) = 4 because A002182(8) = 48 has 10 divisors and the smallest highly composite number with at least 10/2 = 5 divisors is 12, and 48/12 = 4.
a(49) = 0 because A002182(49) = 14414400 has 504 divisors and the smallest highly composite number with at least 504/2 = 252 divisors is 1081080, and 14414400/1081080 equals 40/3, which is not an integer.

Crossrefs

Cf. A002182.

Sequence in context: A166312 A138099 A359634 * A110266 A377107 A349138

Adjacent sequences: A353933 A353934 A353935 * A353937 A353938 A353939

Keyword

nonn

Author

J. Lowell, May 11 2022

Extensions

More terms from Amiram Eldar, May 12 2022

Status

approved