A061481 a(n) = floor(e^(n/e)).

1, 1, 2, 3, 4, 6, 9, 13, 18, 27, 39, 57, 82, 119, 172, 249, 359, 520, 751, 1085, 1568, 2265, 3272, 4727, 6830, 9867, 14255, 20593, 29751, 42980, 62092, 89703, 129591, 187216, 270465, 390733, 564479, 815485, 1178106, 1701972, 2458784, 3552126, 5131643

Offset: 0

Author

Amarnath Murthy, May 05 2001

Keywords

• nonn

Comments

Integer part of the maximal product possible among numbers (not restricted to integers) that sum to n. Note that a(n) >= A000792(n).

Ignoring the first term, for n >= 1, 1,2,3,4,6,9,... is the maximal integer such that its positive real n-th root in an infinite power tower converges to a limit; e.g., for n=5, 6 is the maximal such integer and (6^(1/5))^((6^(1/5))^((6^(1/5))^(...))) converges (to 2.1991359...). Similar infinite power towers with the 5th roots of 1,2,3,4,5, respectively also converge. See comments and links associated with A073229 and A073230. These terms are also the numbers of such converging infinite power towers composed of n-th roots of positive integers. Disregarding the trivial power tower of 1s, 2 is the unique positive integer whose infinite power tower of its square root converges; the limit is 2 itself. - Rick L. Shepherd, Sep 30 2007

Links

• Harry J. Smith, Table of n, a(n) for n = 0..500
• E. F. Krause, Maximizing The Product of Summands, Mathematics Magazine, MAA Oct 1996, Vol. 69, no. 5 pp. 270-271.
• D. J. Newman, A Problem Seminar, Problem 15 pp. 5; 15 Springer-Verlag NY 1982.

Crossrefs

Cf. A107586.

Cf. A073229, A073230.

Programs

Mathematica

Table[ Floor[E^(n/E)], {n, 0, 35}] (* Robert G. Wilson v, Oct 23 2004 *)

PARI

{ default(realprecision, 100); e=exp(1); for (n=0, 500, write("b061481.txt", n, " ", floor(e^(n/e))) ) } \\ Harry J. Smith, Jul 23 2009