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A234515
Natural numbers n sorted by decreasing values of number k(n) = log_n(sigma(n)), where sigma(n) = A000203(n) = the sum of divisors of n.
10
2, 4, 6, 12, 8, 24, 18, 3, 36, 30, 10, 60, 20, 48, 16, 72, 120, 84, 42, 40, 180, 90, 96, 28, 144, 240, 168, 14, 108, 360, 54, 32, 420, 80, 252, 132, 216, 56, 210, 126, 300, 66, 336, 480, 192, 288, 720, 840, 156, 504, 150, 540, 264, 140, 600, 78, 270, 1260, 432
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
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
KEYWORD
nonn,changed
AUTHOR
Jaroslav Krizek, Jan 03 2014
STATUS
approved