|
%I #21 Aug 10 2018 09:21:48
%S 1,1,2,7,8,14,32,121,126,248,512,1003,2048,4064,8176,130539,32768,
%T 65382,131072,261868,524224,1048064,2097152,4193131,8388576,16775168,
%U 33554180,67104688,134217728,268426672,536870912,8589802359,2147482624,4294934528,8589934336,17179801257,34359738368,68719345664,137438949376,274877643724,549755813888
%N Numerators of the positive solution to 2^(n-1) = Sum_{d|n} a(d) * a(n/d).
%C Numerators of rational valued sequence f whose Dirichlet convolution with itself yields function g(n) = A000079(n-1) = 2^(n-1). - _Antti Karttunen_, Aug 10 2018
%H Andrew Howroyd, <a href="/A299151/b299151.txt">Table of n, a(n) for n = 1..1000</a>
%e Sequence begins: 1, 1, 2, 7/2, 8, 14, 32, 121/2, 126, 248, 512, 1003, 2048, 4064, 8176, 130539/8, 32768.
%t nn=50;
%t sys=Table[2^(n-1)==Sum[a[d]*a[n/d],{d,Divisors[n]}],{n,nn}];
%t Numerator[Array[a,nn]/.Solve[sys,Array[a,nn]][[2]]]
%o (PARI)
%o A299151perA299152(n) = if(1==n,n,(2^(n-1)-sumdiv(n,d,if((d>1)&&(d<n),A299151perA299152(d)*A299151perA299152(n/d),0)))/2);
%o A299151(n) = numerator(A299151perA299152(n));
%Y Cf. A000005, A000010, A000740, A018804, A023900, A029935, A034691, A046643, A059966, A228369, A257098, A296302, A298971, A299119, A299149, A299152.
%Y Cf. also A317831.
%K nonn,frac
%O 1,3
%A _Gus Wiseman_, Feb 03 2018
%E More terms from _Antti Karttunen_, Jul 29 2018
|
