A262609 Divisors of 1728.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728

Offset

1,2

Comments

A000578(12) = 1728 is the cube of 12.

The number of divisors of 1728 is A000005(1728) = 28.

The sum of the divisors of 1728 is A000203(1728) = 5080.

The prime factorization of 1728 is 2^6 * 3^3.

1728 + 1 = A001235(1) = A011541(2) = 1729 is the Hardy-Ramanujan number.

Three examples related to cellular automata:

1728 is also the number of ON cells after 32 generations of the cellular automata A160239 and A253088.

1728 is also the total number of ON cells around the central ON cell after 24 generations of the cellular automata A160414 and A256530.

1728 is also the total number of ON cells around the central ON cell after 43 generations of the cellular automata A160172 and A255366.

Links

Table of n, a(n) for n=1..28.

N. J. A. Sloane, Illustration of A160239(32) = A246030(5) = 1728

Index entries for sequences related to divisors of numbers

Example

a(3) * a(26) = 3 * 576 = 1728.
a(4) * a(25) = 4 * 432 = 1728.
a(5) * a(24) = 6 * 288 = 1728.

Mathematica

Divisors[1728]

Prog

(Sage) divisors(1728);
(PARI) divisors(1728)

Crossrefs

Cf. A000005, A000203, A000578, A001235, A011541, A133029, A160172, A160239, A160414, A246030, A253088, A255366, A256530.

Sequence in context: A275199 A003586 A114334 * A018690 A284698 A018452

Adjacent sequences: A262606 A262607 A262608 * A262610 A262611 A262612

Keyword

nonn,fini,full,easy

Author

Omar E. Pol, Nov 20 2015

Status

approved