0,3

Integer part of the maximal product possible amongst 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 comprised 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 (rshepherd2(AT)hotmail.com), Sep 30 2007

E. F. Krause, "Maximizing The Product of Summands", Math. Mag. Vol. 69 no. 5 pp. 270-1 Oct 1996 MAA Washington DC.

D. J. Newman, A Problem Seminar,Problem 15 pp. 5; 15 Springer-Verlag NY 1982.

Harry J. Smith, Table of n, a(n) for n=0,...,500

Table[ Floor[E^(n/E)], {n, 0, 35}] (from 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))) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 23 2009]

Cf. A107586.

Cf. A073229, A073230.

Sequence in context: A098578 A076968 A098889 this_sequence A017824 A094054 A001521

Adjacent sequences: A061478 A061479 A061480 this_sequence A061482 A061483 A061484

nonn

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 05 2001