A141847 Least number k such that sigma_2(k) >= 2^n.

2, 2, 3, 4, 6, 8, 10, 15, 20, 28, 40, 54, 78, 108, 156, 216, 300, 420, 600, 840, 1188, 1680, 2340, 3360, 4680, 6600, 9240, 13200, 18480, 26400, 36960, 52560, 73920, 105000, 147840, 209160, 294840, 415800, 589680, 831600, 1178100, 1663200, 2353680

Offset: 1

Author

T. D. Noe, Jul 11 2008

Keywords

• nonn

Comments

For n-bit arithmetic, m=a(n) - 1 is the largest number for which sigma_2(m) can be computed without overflow. For 31, 32, 63 and 64 bits, the numbers are respectively 36959, 52559, 2389186799 and 3380176799.

Links

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

Crossrefs

Cf. A001157 (sigma_2).

Programs

Mathematica

k=1; Table[While[DivisorSigma[2,k]<2^n, k++ ]; k, {n,40}]

Formula

For large n, a(n) ~ sqrt(2)*a(n-1).