A284711 - OEIS

%I #13 Aug 23 2018 15:53:06

%S 23,86,339,1332,5298,21066,83987,334966,1336988,5338206,21321234,

%T 85176636,340338398,1360073016,5435820051,21727481616,86853790498,

%U 347214198246,1388133456348,5549915835836,22190143855898,88725807876186,354775752246802,1418633882621748,5672803378074548

%N Even bisection of A283848.

%H Robert Israel, <a href="/A284711/b284711.txt">Table of n, a(n) for n = 2..1659</a>

%H Shinsaku Fujita, <a href="https://doi.org/10.1246/bcsj.20160369">alpha-beta Itemized Enumeration of Inositol Derivatives and m-Gonal Homologs by Extending Fujita's Proligand Method</a>, Bull. Chem. Soc. Jpn. 2017, 90, 343-366; doi:10.1246/bcsj.20160369. See Table 8.

%F a(n) = A283848(2*n)=(4*n)^(-1)*Sum_{d|2*n, d even} phi(d)*4^(2*n/d) + 5*2^(2*n-2). - _Robert Israel_, Aug 23 2018 after Fujita (2017), Eq. (101)

%p f:= proc(n) uses numtheory;

%p (4*n)^(-1)*add(phi(d)*4^(2*n/d),d=select(type,divisors(2*n),even))+5*2^(2*n-2)

%p end proc:

%p map(f, [$2..40]);

%o (PARI) A(m,n) = if (m%2, 2^((m-1)/2)*n^((m+1)/2), sumdiv(m, d, ((d%2)==0)*(eulerphi(d)*2^(m/d)*n^(m/d)))/(2*m) + 2^(m/2-2)*n^(m/2)*(2*n+1));

%o lista(nn) = for(n=2, nn, print1(T(2*n, 2), ", ")) \\ _Michel Marcus_, Apr 02 2017

%Y The 8 sequences in Table 8 of Fujita (2017) are A053656, A000011, A256216, A256217, A123045, A283846, A283847, A283848.

%Y The even bisection of A283848 gives A000079.

%K nonn

%O 2,1

%A _N. J. A. Sloane_, Apr 01 2017

%E More terms from _Michel Marcus_, Apr 02 2017

%E Edited by _Robert Israel_, Aug 23 2018