Tuesday, September 07, 2021

[apmaeqcp] chunks of base 36

base 36 can be expressed as 0..9,a..z.  (there is some awkwardness of letters which look like numerals.  we ignore this awkwardness.)

36 conveniently has many divisors:

2*18   0123456789abcdefgh ijklmnopqrstuvwxyz
3*12   0123456789ab cdefghijklmn opqrstuvwxyz
4* 9   012345678 9abcdefgh ijklmnopq rstuvwxyz
6* 6   012345 6789ab cdefgh ijklmn opqrst uvwxyz
9* 4   0123 4567 89ab cdef ghij klmn opqr stuv wxyz
12*3   012 345 678 9ab cde fgh ijk lmn opq rst uvw xyz
18*2   01 23 45 67 89 ab cd ef gh ij kl mn op qr st uv wx yz

aliquot sum = sum of divisors not including itself but including 1 = 55.  36 is therefore an abundant number.

55 or 55+36 = 91 might be a good deck of cards, each card getting one of the letter chunks above.

multiples of divisors, i.e., numbers x such that gcd(36,x) is not 1, can be read off as the first character of each chunk.

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