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 A299151 Numerators of the positive solution to 2^(n-1) = Sum_{d|n} a(d) * a(n/d). 8
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 21 05:37 EDT 2022. Contains 353889 sequences. (Running on oeis4.)