A288443 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.
2, 24, 160, 896, 4608, 22528, 106496, 491520, 2228224, 9961472, 44040192, 192937984, 838860800, 3623878656, 15569256448, 66571993088, 283467841536, 1202590842880, 5085241278464, 21440476741632, 90159953477632, 378231999954944, 1583296743997440, 6614661952700416, 27584547717644288, 114841790497947648
Offset: 0
Programs
-
Magma
[(2*n+1)*2^(2*n+1): n in [0..25]];
-
PARI
a(n) = (2*n+1)<<(2*n+1) \\ Charles R Greathouse IV, Jul 07 2017
Formula
a(n) = (2n + 1)*2^(2n + 1).
a(n) = A036289(2n + 1).
a(n) = A098713(n) + 1.
a(n) = 2*A058962(n). - Joerg Arndt, Jun 25 2017
From Amiram Eldar, Jul 03 2020: (Start)
Sum_{n>=0} 1/a(n) = arctanh(1/2) = log(3)/2 (A156057).
Sum_{n>=0} (-1)^n/a(n) = arctan(1/2) (A073000). (End)