A065549 a(1) = 1; for n > 1, a(n) = 2^((A000043(n) - 1)/2).

2, 4, 8, 64, 256, 512, 32768, 1073741824, 17592186044416, 9007199254740992, 9223372036854775808, 1852673427797059126777135760139006525652319754650249024631321344126610074238976

Offset: 2

Author

Labos Elemer, Nov 13 2001

Keywords

• nonn

Comments

Proper subset of A065405.

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

Positive real roots of 2n^4 - n^2 - A000396(n) = 0 for A000396(n) > 6. - César Aguilera, Nov 11 2018

Links

• Muniru A Asiru, Table of n, a(n) for n = 2..20

Crossrefs

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

Programs

Mathematica

Array[2^((MersennePrimeExponent@ # - 1)/2) &, 12, 2] (* Michael De Vlieger, Aug 25 2018 *)

PARI

lista(nn) = {forprime(p=3, nn, if (isprime(2^p-1), print1(2^((p-1)/2), ", ")););} \\ Michel Marcus, Aug 04 2016

Formula

log(n) is approximately log(sqrt(A000668(n)/2)). - César Aguilera, Nov 11 2018