A299152 Denominators of the positive solution to 2^(n-1) = Sum_{d|n} a(d) * a(n/d).

1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

Sequence begins: 1, 1, 2, 7/2, 8, 14, 32, 121/2, 126, 248, 512, 1003, 2048, 4064, 8176, 130539/8, 32768.

Mathematica

nn=50;
sys=Table[2^(n-1)==Sum[a[d]*a[n/d], {d, Divisors[n]}], {n, nn}];
Denominator[Array[a, nn]/.Solve[sys, Array[a, nn]][[2]]]

Prog

(PARI)
up_to = 65537;
prepareA299151perA299152(up_to) = { my(vmemo = vector(up_to)); for(n=1, up_to, vmemo[n] = if(1==n, n, (2^(n-1)-sumdiv(n, d, if((d>1)&&(d<n), vmemo[d]*vmemo[n/d], 0)))/2)); (vmemo); };
v299151perA299152 = prepareA299151perA299152(up_to);
A299151perA299152(n) = v299151perA299152[n];
\\ Or without memoization as:
A299151perA299152(n) = if(1==n, n, (2^(n-1)-sumdiv(n, d, if((d>1)&&(d<n), A299151perA299152(d)*A299151perA299152(n/d), 0)))/2);
A299152(n) = denominator(A299151perA299152(n)); \\ Antti Karttunen, Jul 29 2018

Crossrefs

Cf. A000005, A000010, A000740, A018804, A023900, A029935, A034691, A046643, A059966, A228369, A257098, A296302, A298971, A299119, A299149, A299151.

Sequence in context: A244226 A344590 A111616 * A332770 A113120 A154843

Adjacent sequences: A299149 A299150 A299151 * A299153 A299154 A299155

Keyword

nonn,frac

Author

Gus Wiseman, Feb 03 2018

Extensions

More terms from Antti Karttunen, Jul 29 2018

Status

approved