A356078 Highly composite numbers that are multiples of their number of divisors.

1, 2, 12, 24, 36, 60, 180, 240, 360, 720, 1260, 1680, 5040, 10080, 15120, 20160, 25200, 55440, 110880, 221760, 277200, 665280, 720720, 1441440, 2882880, 3603600, 8648640, 14414400, 32432400, 43243200, 61261200, 245044800, 551350800, 735134400, 1102701600, 2205403200

Offset

1,2

Comments

Conjecture: this sequence is finite. The prime factorization of the number of divisors of a large highly composite number usually has a high power of 2; this is not true of the number of divisors of a highly composite number itself.

Links

Table of n, a(n) for n=1..36.

Example

180 (in A002182) has 18 divisors, and 180/18 equals 10; so, 180 is in this sequence.

Crossrefs

Intersection of A002182 and A033950.

Cf. A002183.

Sequence in context: A353011 A110821 A262983 * A324508 A100786 A141586

Adjacent sequences: A356075 A356076 A356077 * A356079 A356080 A356081

Keyword

nonn

Author

J. Lowell, Jul 25 2022

Extensions

More terms from Amiram Eldar, Jul 25 2022

Status

approved