The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A033179 Numbers k such that exactly one multiset of k positive integers has equal sum and product. 6
2, 3, 4, 6, 24, 114, 174, 444 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
No other terms below 10^10 (Ecker, 2002). Probably finite and complete.
For any m, there is the multiset {m, 2, 1^(m-2)} with sum and product 2m.
(A) If m-1 is composite (m-1=ab), then {a+1, b+1, 1^(m-2)} is another multiset with sum = product. (Hugo van der Sanden)
(B) If 2m-1 is composite (2m-1=ab), then {2, (a+1)/2, (b+1)/2, 1^(m-3)} is another such multiset. (Don Reble)
(C) If m = 30j+12, then {2, 2, 2, 2, 2j+1, 1^(30j+7)} is another such multiset. (Don Reble)
Conditions (A), (B), (C) eliminate all k's except for 2, 3, 4, 6, 30j+0, and 30j+24.
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 174, p. 54, Ellipses, Paris 2008.
R. K. Guy, 'Unsolved Problems in Number Theory' (Section D24).
LINKS
Michael W. Ecker, When Does a Sum of Positive Integers Equal Their Product? Mathematics Magazine 75(1), 2002, pp. 41-47.
Piotr Miska and Maciej Ulas, On the Diophantine equation sigma_2(Xn)=sigma_n(Xn), arXiv:2203.03942 [math.NT], 2022.
CROSSREFS
Cf. A033178.
Sequence in context: A217442 A065199 A249156 * A067244 A084811 A051856
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
Revised by Don Reble, Jun 11 2005
Edited by Max Alekseyev, Nov 13 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 09:54 EDT 2024. Contains 372620 sequences. (Running on oeis4.)