A094086 Babylonian reciprocals - factors needed to turn an ugly number into a power of sixty.

60, 30, 20, 15, 12, 10, 450, 400, 6, 5, 4, 225, 200, 3, 150, 144, 8000, 2, 6750, 100, 90, 80, 75, 72, 4000, 1, 3375, 50, 48, 45, 160000, 40, 2250, 36, 2000, 30, 1728, 101250, 1600, 25, 24, 1350, 80000, 20, 1125, 18, 1000, 16, 15, 3200000, 864, 50625, 800, 750

Offset

1,1

Comments

Although the Babylonians did not have zero or a decimal point or even a decimal number system, they could calculate fractions, even square and cube roots quite accurately. "30" could mean either thirty or 30/60 = 1/2 or 30/3600 = 1/120 or other such fractions. It would be as if we expressed decimals without zeros or decimal points - 1/2 = 5, 1/4 = 25, 1/8 = 125, 1/10 = 1, etc.

Links

Table of n, a(n) for n=1..54.

Formula

a(n) = (60^x)/f(z) where f(z) = A051037 and 60^(x - 1) > n > 60^x

Example

a(31) = 160000 because the 31st ugly number, f(31) = 81 and (60^4)/81 = 160000

Crossrefs

Cf. A051037.

Sequence in context: A341293 A133000 A033380 * A206480 A230742 A112025

Adjacent sequences: A094083 A094084 A094085 * A094087 A094088 A094089

Keyword

easy,nonn

Author

Michael Joseph Halm, May 01 2004

Status

approved