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

0,3

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A107586.

Cf. A073229, A073230.

Sequence in context: A238430 A285484 A098889 * A017824 A343942 A094054

Adjacent sequences: A061478 A061479 A061480 * A061482 A061483 A061484

Keyword

nonn

Author

Amarnath Murthy, May 05 2001

Status

approved