A033178 - OEIS

A033178

Number of multisets of n positive integers with equal sum and product.

1, 1, 1, 3, 1, 2, 2, 2, 2, 3, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 1, 5, 4, 3, 3, 5, 2, 4, 3, 5, 2, 3, 2, 6, 3, 3, 4, 7, 2, 5, 2, 4, 4, 5, 2, 5, 4, 4, 3, 7, 2, 5, 4, 5, 4, 4, 2, 9, 3, 4, 4, 7, 2, 5, 5, 4, 3, 6, 3, 9, 4, 3, 3, 6, 3, 5, 2, 7, 4, 5, 2, 10, 5, 4, 5, 8, 2, 6, 3, 6, 3, 6, 5, 6, 5, 4, 5, 8, 3, 6, 3, 5

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OFFSET

2,4

COMMENTS

The multiset {n^1, 2^1, 1^(n-2)} has n elements and sum = product = 2n. Hence a(n) >= 1.

REFERENCES

R. K. Guy, 'Unsolved Problems in Number Theory' (Section D24).

LINKS

David Radcliffe, Table of n, a(n) for n = 2..10000

Onno M. Cain, Bioperational Multisets in Various Semi-rings, arXiv:1908.03235 [math.RA], 2019.

L. Kurlandchik and A. Nowicki, When the sum equals the product, The Mathematical Gazette, 84(499) (2000), 91-94. doi:10.2307/3621488.

Burkard Polster, What's the next freak identity? A new deep connection with Sophie Germain primes, YouTube Mathologer video, 2024.