cp's OEIS Frontend

The divisors of 24 greater than 1 are the only positive integers n with the property m^2 == 1 (mod n) for all integer m coprime to n. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 10 2001

Numbers n for which all Dirichlet characters are real. - Benoit Cloitre, Apr 21 2002

These are the numbers n that are divisible by all numbers less than or equal to the square root of n. - Tanya Khovanova, Dec 10 2006 [For a proof, see the Tauvel paper in references. - Bernard Schott, Dec 20 2012]

Also, numbers n such that A160812(n) = 0. - Omar E. Pol, Jun 19 2009

It appears that these are the only positive integers n such that A160812(n) = 0. - Omar E. Pol, Nov 17 2009

24 is a highly composite number: A002182(6)=24. - Reinhard Zumkeller, Jun 21 2010

Chebolu points out that these are exactly the numbers for which the multiplication table of the integers mod n have 1s only on their diagonal, i.e., ab == 1 (mod n) implies a = b (mod n). - Charles R Greathouse IV, Jul 06 2011

It appears that 3, 4, 6, 8, 12, 24 (the divisors >= 3 of 24) are also the only numbers n whose proper non-divisors k are prime numbers if k = d-1 and d divides n. - Omar E. Pol, Sep 23 2011

About the last Pol's comment: I have searched to 10^7 and have found no other terms. - Robert G. Wilson v, Sep 23 2011

Sum_{i=1..8} A000005(a(i))^3 = (Sum_{i=1..8} A000005(a(i)))^2, see Kordemsky in References and Barbeau et al. in Links section. - Bruno Berselli, Dec 29 2014

48 is a highly composite number: A002182(8)=48. - Reinhard Zumkeller, Jun 21 2010

These are the orders, without repetition, of the finite subgroups of GL_3(Z); see Conway and Sloane. - Hal M. Switkay, Nov 06 2023

Comment from J. Lowell: Regular polygons with n sides in which internal angles have integral number of degrees (n >= 3).

360 is a highly composite number: A002182(13) = 360. - Reinhard Zumkeller, Jun 21 2010

There are 22209 ways to represent 360 as a sum of its distinct divisors (A033630). That's more than any smaller number, hence 360 is in A065218. - Alonso del Arte, Oct 09 2017

36 is a highly composite number: A002182(7)=36. - Reinhard Zumkeller, Jun 21 2010

Numbers with all prime indices and exponents <= 2. Reversing inequalities gives A062739, strict A353502. - Gus Wiseman, Jun 28 2022

Sequence is finite with last term a(12) = 60; A000005(60) = 12. - Reinhard Zumkeller, Dec 08 2009.

60 is a highly composite number: A002182(9) = 60. - Reinhard Zumkeller, Jun 21 2010

There are 35 ways to partition 60 as a sum of its distinct divisors (see A033630). This is more than any smaller number (hence 60 is listed in A065218). - Alonso del Arte, Oct 12 2017

720 is a highly composite number: A002182(14)=720. - Reinhard Zumkeller, Jun 21 2010

2520 is the largest and last of most highly composite numbers = A072938(7) = A002182(18) = 2520;

a(A000005(2520)) = a(48) = 2520 is the last term.

A242627(2520*n) = 9. - Reinhard Zumkeller, Jul 16 2014

27720 is a highly composite number: A002182(25)=27720;

the sequence is finite with A002183(25)=96 terms: a(96)=27720.

120 is a highly composite number: A002182(10) = 120. - Reinhard Zumkeller, Jun 21 2010

120 is the first 3-perfect number: A005820(1) = 120. - Michel Marcus, Nov 21 2015

There are 279 ways to partition 120 as a sum of its distinct divisors (see A033630). This is more than any smaller number (hence 120 is listed in A065218). - Alonso del Arte, Oct 12 2017

240 is a highly composite number: A002182(12) = 240. - Reinhard Zumkeller, Jun 21 2010

There are 2158 ways to partition 240 as a sum of some of its distinct divisors (see A033630). This is more than any smaller number (hence 240 is listed in A065218). - Alonso del Arte, Dec 20 2017