Number in harmonic division

A number in harmonic division , is a number whose dividers, put in harmonic Rapport, give an entirety. The first small numbers in harmonic division are:

1, 6, 28, 140, 270, 496, 672,1638,2970,6200, 8128, 8190

Three of the listed numbers are also perfect numbers, and like the perfect numbers, the numbers in harmonic division tend to being even numbers, at least in the interval observed. In 1972, W.H. Mills showed that except 1, there does not exist number in harmonic division with factors first lower than 10⁷.

For example, 496 is a number in harmonic division because 496 divided by the nap of the opposite from its dividers, 1,2,4,8,16,31,62,124,248 and 496, (the harmonic report/ratio), gives an entirety, 1 in this case.

See too

• primitive semi-perfect Number

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