A172516 Least number k such that sigma(k) >= 2^n.

2, 3, 6, 10, 18, 30, 60, 108, 180, 360, 720, 1260, 2520, 5040, 9240, 17640, 35280, 65520, 131040, 257040, 498960, 982800, 1884960, 3603600, 7207200, 14414400, 28274400, 56548800, 110270160, 220540320, 428828400, 845404560, 1690809120

Offset: 1

Author

T. D. Noe, Feb 05 2010

Keywords

• nonn

Comments

For n-bit arithmetic, m=a(n)-1 is the largest number for which sigma(m) can be computed without overflow. This is a subsequence of the highly abundant numbers, A002093, which is very useful for computing this sequence. a(63) is 1454751268447276800.

Links

• T. D. Noe, Table of n, a(n) for n=1..64

Crossrefs

A141847 (least number k such that sigma2(k) >= 2^n)

Programs

Mathematica

k=1; Table[While[DivisorSigma[1,k]<2^n, k++ ]; k, {n,20}]

Formula

a(n) <= 2 * a(n-1)