A134713 Base-2 logarithm of (n-th even superperfect number divided by 2^n), plus 1.

1, 1, 2, 3, 8, 11, 12, 23, 52, 79, 96, 115, 508, 593, 1264, 2187, 2264, 3199, 4234, 4403, 9668, 9919, 11190, 19913, 21676, 23183, 44470, 86215, 110474, 132019, 216060, 756807, 859400, 1257753, 1398234, 2976185, 3021340, 6972555, 13466878

Offset: 1

Author

Omar E. Pol, Nov 07 2007

Keywords

• nonn

Examples

			a(5) = 8 because the 5th even superperfect number is 4096, 2^5 = 32, 4096/32 = 128, log_2(128) = 7 (because 2^7 = 128) and 7+1 = 8.
		

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]] (* Amiram Eldar, Oct 21 2024 *)

Formula

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