A291713 -id:A291713 - cp's OEIS frontend

A114334 Divisors of 6^6.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 432, 486, 576, 648, 729, 864, 972, 1296, 1458, 1728, 1944, 2592, 2916, 3888, 5184, 5832, 7776, 11664, 15552, 23328, 46656

Offset: 1

Reinhard Zumkeller, Feb 07 2006

Subsequence of A003586; 128 = 2^(6+1) is the smallest 3-smooth number not dividing 6^6.

a(49) = A175755(1) = 46656 = smallest number with exactly 49 divisors; a(7) = A201266(1). - Reinhard Zumkeller, Nov 29 2011

Index entries for sequences related to divisors of numbers

A291713 lists terms a(14)-a(22).

a114334 n = a114334_list !! (n-1)
a114334_list = a027750_row (6 ^ 6)  -- Reinhard Zumkeller, Jan 07 2014

Divisors[6^6] (* Robert G. Wilson v, Aug 17 2012 *)

divisors(6^6) \\ Charles R Greathouse IV, Jun 21 2017

a(n) = A027750(46656,n) for n = 1 .. A000005(46656). - Reinhard Zumkeller, Jan 07 2014

A291714 2520 * preferred ratios of room height / length in Alberti's Ten Books on Architecture.

Original entry on oeis.org

1260, 1575, 1680, 1890, 2016, 2100, 2205, 2520

Offset: 1

Hugo Pfoertner, Sep 01 2017

			a(8)=2205 is in the sequence, because the length / height ratio of 2520/2205 corresponds to the referred ratio of 8/7 given in the table provided in A291713.

Radislav Zuk, From Renaissance Musical Proportions to Polytonality in Twentieth Century Architecture, Chapter 38 in Volume 1 of K. Williams and M. J. Ostwald (eds.), Architecture and Mathematics from Antiquity to the Future, DOI 10.1007/978-3-319-00137-1_38, Springer International Publishing Switzerland 2015

Cf. A291713, A291715, A291719.

A291715 a(n) = 420*(preferred ratios of room width / height in Alberti's Ten Books on Architecture).

Original entry on oeis.org

210, 252, 280, 315, 336, 350, 360, 420

Offset: 1

Hugo Pfoertner, Sep 01 2017

			a(5)=336 is in the sequence, because the height / width ratio of 420 / 336 corresponds to the preferred ratio of H:W = 5:4 provided in the table given in A291713.

Radislav Zuk, From Renaissance Musical Proportions to Polytonality in Twentieth Century Architecture, Chapter 38 in Volume 1 of K. Williams and M. J. Ostwald (eds.), Architecture and Mathematics from Antiquity to the Future, DOI 10.1007/978-3-319-00137-1_38, Springer International Publishing Switzerland 2015

Cf. A291713, A291714, A291719.

cp's OEIS Frontend

A114334 Divisors of 6^6.

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A291714 2520 * preferred ratios of room height / length in Alberti's Ten Books on Architecture.

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A291715 a(n) = 420*(preferred ratios of room width / height in Alberti's Ten Books on Architecture).

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