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A065549
a(1) = 1; for n > 1, a(n) = 2^((A000043(n) - 1)/2).
4
2, 4, 8, 64, 256, 512, 32768, 1073741824, 17592186044416, 9007199254740992, 9223372036854775808, 1852673427797059126777135760139006525652319754650249024631321344126610074238976
OFFSET
2,1
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
FORMULA
log(n) is approximately log(sqrt(A000668(n)/2)). - César Aguilera, Nov 11 2018
MATHEMATICA
Array[2^((MersennePrimeExponent@ # - 1)/2) &, 12, 2] (* Michael De Vlieger, Aug 25 2018 *)
PROG
(PARI) lista(nn) = {forprime(p=3, nn, if (isprime(2^p-1), print1(2^((p-1)/2), ", ")); ); } \\ Michel Marcus, Aug 04 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 13 2001
STATUS
approved