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A094086 Babylonian reciprocals - factors needed to turn an ugly number into a power of sixty. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A202561 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

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Last modified May 23 08:03 EDT 2017. Contains 286909 sequences.