A234519 Natural numbers n sorted by decreasing values of number k(n) = sigma(n)^(1/n), where sigma(n) = A000203(n) = the sum of divisors of n.

2, 4, 3, 6, 5, 8, 7, 10, 9, 12, 14, 11, 16, 15, 18, 13, 20, 24, 17, 21, 22, 19, 28, 26, 30, 23, 25, 27, 32, 36, 34, 33, 29, 40, 31, 35, 42, 38, 39, 44, 48, 37, 45, 46, 41, 50, 54, 52, 43, 56, 60, 51, 49, 47, 55, 58, 57, 64, 66, 53, 63, 62, 72, 68, 70, 59, 65

Offset

1,1

Comments

Number k(n) = sigma(n)^(1/n) is number such that k(n)^n = sigma(n).

For number 2; k(2) = sigma(2)^(1/2) = sqrt(3) = 1,732050807568… = A002194 (maximal value of function k(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 A234521 - 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..1000

Prog

(PARI) a(n)=vecsort(vector(2*n, i, sigma(i)^(1/i)), , 5)[n] \\ Michel Marcus and Ralf Stephan, Jan 14 2014

Crossrefs

Cf. A234515, A234516, A234517, A234518, A234520, A234521, A234522, A234523, A234524.

Sequence in context: A217560 A114112 A113981 * A289726 A308598 A343012

Adjacent sequences: A234516 A234517 A234518 * A234520 A234521 A234522

Keyword

nonn

Author

Jaroslav Krizek, Jan 04 2014

Status

approved