OFFSET
2,1
COMMENTS
Each term gives the largest of the N-1 terms in A050210 corresponding to the fractions with denominator N.
REFERENCES
Guy, R. K. "Egyptian Fractions." section D11 in "Unsolved Problems in Number Theory", 2nd ed. New York: Springer-Verlag, pp. 158-166, 1994.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 2..198
Robert Munafo, Largest Denominator of Greedy Egyptian Fraction Sum for M/N
Eric Weisstein's World of Mathematics, Egyptian Fractions.
EXAMPLE
Consider a(5). There are 4 fractions with 5 in the denominator: 1/5=1/5, 2/5=1/3+1/15, 3/5=1/2+1/10 and 4/5=1/2+1/4+1/20. Of these, the largest denominator is 20, so a(5)=20.
PROG
(Maxima) /* MACSYMA or maxima */ egypt(x) := block([i, n, d, p, e, on, od], ( n : num(x), d : n/x, on : n, od : d, p : 0, e : [], for i:1 while x>0 do ( n : num(x), d : n/x, p : fix((d+n-1)/n), x : x - 1/p, e : append(e, [p]) ), return(p) ) ); for b:2 step 1 through 100 do ( max:2, for a:2 step 1 through b-1 do ( if gcd(a, b)=1 then ( m : egypt(a/b), if m>max then max : m ) ), print("a[", b, "]=", max) ), t$
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Munafo, Nov 06 2004
EXTENSIONS
a(6) corrected by Seiichi Manyama, Sep 18 2022
STATUS
approved