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A033178 Number of multisets of n positive integers with equal sum and product. 6
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 (list; graph; refs; listen; history; text; internal format)
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.

CROSSREFS

Cf. A033179, A104173.

Sequence in context: A305516 A305182 A291047 * A029418 A185736 A144148

Adjacent sequences:  A033175 A033176 A033177 * A033179 A033180 A033181

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 2 20:22 EST 2020. Contains 338891 sequences. (Running on oeis4.)