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Multiamicable Numbers


Two integers n and m<n are (alpha,beta)-multiamicable if

 sigma(m)-m=alphan

and

 sigma(n)-n=betam,

where sigma(n) is the divisor function and alpha,beta are positive integers. If alpha=beta=1, (m,n) is an amicable pair.

m cannot have just one distinct prime factor, and if it has precisely two distinct prime factors, then alpha=1 and m is even. Small multiamicable numbers for small alpha,beta are given by Cohen et al. (1995). Several of these numbers are reproduced in the table below.

alphabetamn
1676455288183102192
1752920152280
171622556040580280
1790863136227249568
171622556040580280
1770821324288177124806144
17199615613902848499240550375424

See also

Amicable Pair, Divisor Function

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References

Cohen, G. L; Gretton, S.; and Hagis, P. Jr. "Multiamicable Numbers." Math. Comput. 64, 1743-1753, 1995.

Referenced on Wolfram|Alpha

Multiamicable Numbers

Cite this as:

Weisstein, Eric W. "Multiamicable Numbers." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MultiamicableNumbers.html

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