

A323725


a(n) is the last (and thus largest) denominator of an Egyptian fraction representing n, where each consecutive denominator is as small as possible.


1




OFFSET

1,2


COMMENTS

Values grow extremely quickly, a(5) has 142548 decimal digits.
The denominators for n = 3 are given in A140335.
The denominators for n = 4 are given in A281873.
The number of terms in the representation of n is A306349(n).


LINKS



EXAMPLE

a(3) = 57960 because (1/1) + (1/2) + (1/3) + (1/4) + (1/5) + (1/6) + (1/7) + (1/8) + (1/9) + (1/10) + (1/15) + (1/230) + (1/57960) = 3 and the final and greatest denominator is 57960. (Sequence A140335 has the full list of denominators.)


PROG

(PARI) a(n)={my(s=n, k=1); while(s>1/k, s=1/k; k++); while(s!=0, k=ceil(1/s); s=1/k); k} \\ Andrew Howroyd, Sep 01 2019
(Python)
from sympy import egyptian_fraction


CROSSREFS

A140335 and A281873 are the denominatorial sequences for 3 and 4, respectively.


KEYWORD

nonn


AUTHOR



STATUS

approved



