# Product and Power Type Amicable Numbers

In the history, there are numbers known by Amicable numbers  (see Madachy, 1966, p. 155). There are many different ways of expressing these numbers. Most famous among them is with operation of addition, such as 220 and 284. In this case the summing the divisors of one we get another number. But there are other type of amicable numbers too ((see Madachy, 1966, pp. 165-167).  Thus, there are many ways of writing amicable numbers.  One with divisions and sums. The other with pair of powers of each other. There is another way to represent is product-type. In this paper, we brings amicable numbers in pairs in terms of products and powers. The idea of  self-amicable numbers is also introduced. Few blokcs of symmetrical amicable numbers multiples of 10 are also given. Some interesting patterns among amicable numbers are also given. For more details below is link for download the complete work:

Complete Work: Product and Power Type Amicable Numbers

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Complete Work: Product and Power Type Amicable Numbers

Also see; I.J. TANEJA,  Amicable Numbers With Patterns in Products and Powers, Zenodo, Open Access. March 05, 2019, pp. 1-25, http://doi.org/10.5281/zenodo.2583306.