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Bisection of A000016 (also of A000013).
4

%I #21 Feb 22 2023 01:42:57

%S 1,2,4,10,30,94,316,1096,3856,13798,49940,182362,671092,2485534,

%T 9256396,34636834,130150588,490853416,1857283156,7048151672,

%U 26817356776,102280151422,390937468408,1497207322930,5744387279818,22076468764192

%N Bisection of A000016 (also of A000013).

%H Seiichi Manyama, <a href="/A026119/b026119.txt">Table of n, a(n) for n = 0..1666</a>

%F a(n) = (Sum_{d | 2n+1} phi(d)*2^((2n+1)/d)) / (4n+2).

%o (PARI) a(n) = sumdiv(2*n+1, d, eulerphi(d)*2^((2*n+1)/d)) / (4*n+2); \\ _Michel Marcus_, Sep 11 2013

%o (Python)

%o from sympy import totient, divisors

%o def A026119(n):

%o m = (n<<1)+1

%o return sum(totient(d)<<m//d-1 for d in divisors(m,generator=True))//m # _Chai Wah Wu_, Feb 21 2023

%Y Cf. A000013, A000016, A000116.

%Y Bisection of A053634 and A053656.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Apr 12 2000