A299151 Numerators of the positive solution to 2^(n-1) = Sum_{d|n} a(d) * a(n/d).

1, 1, 2, 7, 8, 14, 32, 121, 126, 248, 512, 1003, 2048, 4064, 8176, 130539, 32768, 65382, 131072, 261868, 524224, 1048064, 2097152, 4193131, 8388576, 16775168, 33554180, 67104688, 134217728, 268426672, 536870912, 8589802359, 2147482624, 4294934528, 8589934336, 17179801257, 34359738368, 68719345664, 137438949376, 274877643724, 549755813888

Offset

1,3

Comments

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

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}];
Numerator[Array[a, nn]/.Solve[sys, Array[a, nn]][[2]]]

Prog

(PARI)
A299151perA299152(n) = if(1==n, n, (2^(n-1)-sumdiv(n, d, if((d>1)&&(d<n), A299151perA299152(d)*A299151perA299152(n/d), 0)))/2);
A299151(n) = numerator(A299151perA299152(n));

Crossrefs

Cf. A000005, A000010, A000740, A018804, A023900, A029935, A034691, A046643, A059966, A228369, A257098, A296302, A298971, A299119, A299149, A299152.

Cf. also A317831.

Sequence in context: A063771 A064293 A063729 * A023178 A334227 A080572

Adjacent sequences: A299148 A299149 A299150 * A299152 A299153 A299154

Keyword

nonn,frac

Author

Gus Wiseman, Feb 03 2018

Extensions

More terms from Antti Karttunen, Jul 29 2018

Status

approved