A134712 Base-2 logarithm of (n-th even superperfect number divided by 2^n).

0, 0, 1, 2, 7, 10, 11, 22, 51, 78, 95, 114, 507, 592, 1263, 2186, 2263, 3198, 4233, 4402, 9667, 9918, 11189, 19912, 21675, 23182, 44469, 86214, 110473, 132018, 216059, 756806, 859399, 1257752, 1398233, 2976184, 3021339, 6972554, 13466877

Offset: 1

Author

Omar E. Pol, Nov 07 2007

Keywords

• nonn

Examples

			a(5) = 7 because the 5th even superperfect number is 4096, 2^5 = 32, 4096/32 = 128 and log_2(128) = 7 (because 2^7 = 128).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..48
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Crossrefs

Cf. A000043, A000396, A000668, A019279, A061652, A090748, A133028.

Programs

Mathematica

With[{max = 48}, MersennePrimeExponent[Range[max]] - Range[max] - 1] (* Amiram Eldar, Oct 21 2024 *)

Formula

a(n) = log_2(A061652(n)/(2^n)) = A000043(n) - n - 1 = A090748(n) - n.