OFFSET
1,1
COMMENTS
Number k(n) = log_n(sigma(n)) = log(sigma(n)) / log(n) is number such that n^k(n) = sigma(n).
The last term of this infinite sequence is number 1, k(1) = 1 (minimal value of function k(n)).
Conjecture: Every natural number n has a unique value of number k(n).
See A234517 - sequence of numbers a(n) such that a(n) > a(k) for all k < n.
LINKS
Jaroslav Krizek, Table of n, a(n) for n = 1..200
EXAMPLE
For number 2; k(2) = log_2(sigma(2)) = log_2(3) = 1,5849625007… = A020857 (maximal value of function k(n)).
PROG
(PARI) lista(nn=100000) = {v = vector(nn, n, if (n==1, 0, log(sigma(n))/log(n))); v = vecsort(v, , 5); for (i=1, 80, print1(v[i], ", ")); } \\ Michel Marcus, Dec 11 2014
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Jaroslav Krizek, Jan 03 2014
STATUS
approved