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

Author

Omar E. Pol, Nov 20 2015

Keywords

• nonn
• fini
• full
• easy

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.

Examples

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

Links

• N. J. A. Sloane, Illustration of A160239(32) = A246030(5) = 1728
• Index entries for sequences related to divisors of numbers

Crossrefs

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

Programs

Mathematica

Divisors[1728]

PARI

divisors(1728)

Sage

divisors(1728);