On an extended divisor product
summatory function
Abstract: It has been conjectured that the sequence of integers whose product of (positive) divisors is larger than that of any smaller number (OEIS A034287) is identical to the sequence of largely composite numbers (OEIS A067128). This paper approaches this conjecture. Furthermore, the summatory function 𝜬(𝑛) is defined as the sum of the 𝑛 first divisor products (extended to include negative divisors), see OEIS A224914. It is conjectured that 𝜬(𝑛) > 0 for all 𝑛 > 47. Two new concepts, highly divisorial-positive numbers and highly divisorial-negative numbers, are introduced.
Publication year: 2023. Format: A4/PDF. Pages: 11.
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