A288443 - OEIS

%I #27 Sep 08 2022 08:46:19

%S 2,24,160,896,4608,22528,106496,491520,2228224,9961472,44040192,

%T 192937984,838860800,3623878656,15569256448,66571993088,283467841536,

%U 1202590842880,5085241278464,21440476741632,90159953477632,378231999954944,1583296743997440,6614661952700416,27584547717644288,114841790497947648

%N a(n) = (2n + 1)*2^(2n + 1); numbers k such that v(k)*2^v(k) = k, where v(n) = A007814(n) is 2-adic valuation of n.

%F a(n) = (2n + 1)*2^(2n + 1).

%F a(n) = A036289(2n + 1).

%F a(n) = A098713(n) + 1.

%F a(n) = 2*A058962(n). - _Joerg Arndt_, Jun 25 2017

%F From _Amiram Eldar_, Jul 03 2020: (Start)

%F Sum_{n>=0} 1/a(n) = arctanh(1/2) = log(3)/2 (A156057).

%F Sum_{n>=0} (-1)^n/a(n) = arctan(1/2) (A073000). (End)

%o (Magma) [(2*n+1)*2^(2*n+1): n in [0..25]];

%o (PARI) a(n) = (2*n+1)<<(2*n+1) \\ _Charles R Greathouse IV_, Jul 07 2017

%Y Cf. A007814, A058962, A098713, A286683.

%Y Odd bisection of A036289.

%Y Cf. A073000, A156057.

%K nonn,easy

%O 0,1

%A _Juri-Stepan Gerasimov_, Jun 24 2017