Number Theory

    

Smallest Numbers Whose Number of Divisors Is a Perfect Number

Authors: Waldemar Puszkarz

We present a formula for the smallest possible numbers whose number of divisors is the $n$-th perfect number. The formula, that produces an integer sequence $a(n)$, involves the $n$-th Mersenne prime that appears both in an exponent of a power of 2 and in the product of consecutive odd primes (the odd primorial). While smallest in some sense, these numbers are among largest one can run into through an exercise in elementary number theory.

Comments: 3 Pages. Originally published on Research Gate in March 2020.

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Submission history

[v1] 2020-12-23 11:19:56
[v2] 2023-08-11 11:19:49

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