A018255 Divisors of 30.

1, 2, 3, 5, 6, 10, 15, 30

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full
• easy

Comments

For n > 1, These are also numbers m such that k^4 + (k+1)^4 + ... + (k + m - 1)^4 is prime for some k and numbers m such that k^8 + (k+1)^8 + ... + (k + m - 1)^8 is prime for some k. - Derek Orr, Jun 12 2014

These seem to be the numbers m such that tau(n) = n*sigma(n) mod m for all n. See A098108 (mod 2), A126825 (mod 3), and A126832 (mod 5). - Charles R Greathouse IV, Mar 17 2022

The squarefree 5-smooth numbers: intersection of A051037 and A005117. - Amiram Eldar, Sep 26 2023

Examples

			From the second comment: 1^3 + 2^3 + 2^3 + 2^3 + 4^3 + 4^3 + 4^3 + 8^3 = (1 + 2 + 2 + 2 + 4 + 4 + 4 + 8)^2 = 729. - _Bruno Berselli_, Dec 28 2014
		

References

• Boris A. Kordemsky, The Moscow Puzzles: 359 Mathematical Recreations, C. Scribner's Sons (1972), Chapter XIII, Paragraph 349.

Links

• Edward Barbeau and Samer Seraj, Sum of Cubes is Square of Sum, arXiv:1306.5257 [math.NT], 2013.
• Index entries for sequences related to divisors of numbers.

Crossrefs

Cf. A000005, A005117, A051037, A158649, A161715.

Cf. A098108, A126825, A126832.

Programs

Magma

Divisors(30); // Bruno Berselli, Dec 28 2014

Mathematica

Divisors[30] (* Vladimir Joseph Stephan Orlovsky, Dec 04 2010 *)

PARI

divisors(30)

Formula

a(n) = A161715(n-1). - Reinhard Zumkeller, Jun 21 2009

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 28 2014