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

Author

T. D. Noe, Mar 23 2009

Keywords

• nonn

Comments

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

Examples

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

Programs

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]
				

Formula

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