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A262609 Divisors of 1728.

%I A262609 #33 Oct 13 2019 18:05:56
%S A262609 1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,96,108,144,192,216,
%T A262609 288,432,576,864,1728
%N A262609 Divisors of 1728.
%C A262609 A000578(12) = 1728 is the cube of 12.
%C A262609 The number of divisors of 1728 is A000005(1728) = 28.
%C A262609 The sum of the divisors of 1728 is A000203(1728) = 5080.
%C A262609 The prime factorization of 1728 is 2^6 * 3^3.
%C A262609 1728 + 1 = A001235(1) = A011541(2) = 1729 is the Hardy-Ramanujan number.
%C A262609 Three examples related to cellular automata:
%C A262609 1728 is also the number of ON cells after 32 generations of the cellular automata A160239 and A253088.
%C A262609 1728 is also the total number of ON cells around the central ON cell after 24 generations of the cellular automata A160414 and A256530.
%C A262609 1728 is also the total number of ON cells around the central ON cell after 43 generations of the cellular automata A160172 and A255366.
%H A262609 N. J. A. Sloane, <a href="/A160239/a160239_1.png">Illustration of A160239(32) = A246030(5) = 1728</a>
%H A262609 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%e A262609 a(3) * a(26) = 3 * 576 = 1728.
%e A262609 a(4) * a(25) = 4 * 432 = 1728.
%e A262609 a(5) * a(24) = 6 * 288 = 1728.
%t A262609 Divisors[1728]
%o A262609 (Sage) divisors(1728);
%o A262609 (PARI) divisors(1728)
%Y A262609 Cf. A000005, A000203, A000578, A001235, A011541, A133029, A160172, A160239, A160414, A246030, A253088, A255366, A256530.
%K A262609 nonn,fini,full,easy
%O A262609 1,2
%A A262609 _Omar E. Pol_, Nov 20 2015