A158661 Least number k such that sigma_n(k) > sigma_n(k+1), where sigma_n(k) = sum of the n-th powers of the divisors of k.

4, 4, 6, 24, 60, 144, 360, 852, 1968, 4488, 10068, 22272, 48780, 105948, 228588, 490404, 1046976, 2225964, 4715400, 9956976, 20965212, 44031360, 92262348, 192920784, 402629256, 838827576, 1744784388, 3623814864, 7516104564

Offset

0,1

Comments

It appears that the inequality a(n+1) > (2+2/n)*a(n) is true for n > 4.

Links

Table of n, a(n) for n=0..28.

Formula

For n>0, a(n) = A098475(n) - 1.

Example

The values of the sigma_3 function (A001158) are increasing up to 25. Hence a(3)=24.

Mathematica

Join[{4, 4}, Table[k=Floor[NSolve[Zeta[n](x-1)^n==x^n, x, WorkingPrecision->100][[ -1, 1, 2]]]; While[DivisorSigma[n, k]<DivisorSigma[n, k+1], k++ ]; k, {n, 2, 30}]]

Crossrefs

Sequence in context: A128089 A019176 A143391 * A264578 A261146 A368304

Adjacent sequences: A158658 A158659 A158660 * A158662 A158663 A158664

Keyword

nonn

Author

T. D. Noe, Mar 23 2009

Status

approved