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a(1) = 1; for n > 1, a(n) = 2^((A000043(n) - 1)/2).
4

%I #68 May 11 2020 03:56:19

%S 2,4,8,64,256,512,32768,1073741824,17592186044416,9007199254740992,

%T 9223372036854775808,

%U 1852673427797059126777135760139006525652319754650249024631321344126610074238976

%N a(1) = 1; for n > 1, a(n) = 2^((A000043(n) - 1)/2).

%C Proper subset of A065405.

%C These values also relate to the sequence of perfect numbers. Every even perfect number except 6 can be written as Sum_{k=1..a(n)} (2*k-1)^3. - _Derek Orr_, Sep 28 2013

%C Positive real roots of 2n^4 - n^2 - A000396(n) = 0 for A000396(n) > 6. - _César Aguilera_, Nov 11 2018

%H Muniru A Asiru, <a href="/A065549/b065549.txt">Table of n, a(n) for n = 2..20</a>

%F log(n) is approximately log(sqrt(A000668(n)/2)). - _César Aguilera_, Nov 11 2018

%t Array[2^((MersennePrimeExponent@ # - 1)/2) &, 12, 2] (* _Michael De Vlieger_, Aug 25 2018 *)

%o (PARI) lista(nn) = {forprime(p=3, nn, if (isprime(2^p-1), print1(2^((p-1)/2), ", ")););} \\ _Michel Marcus_, Aug 04 2016

%Y Cf. A000043, A065403, A065404, A065405, A000396.

%K nonn

%O 2,1

%A _Labos Elemer_, Nov 13 2001