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.

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

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

Cf. A234516, A234517, A234518, A234519, A234520, A234521, A234522, A234523, A234524.

Sequence in context: A057700 A337182 A236020 * A136103 A182235 A180304

Adjacent sequences: A234512 A234513 A234514 * A234516 A234517 A234518

Keyword

nonn

Author

Jaroslav Krizek, Jan 03 2014

Status

approved