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A014668
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a(1) = 1, a(n) = Sum_{k=1..n-1} Sum_{d|k} a(d).
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3
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1, 1, 3, 7, 16, 33, 71, 143, 295, 594, 1206, 2413, 4871, 9743, 19559, 39138, 78428, 156857, 314047, 628095, 1256809, 2513693, 5028594, 10057189, 20116979, 40233975, 80472823, 160945945, 321901713, 643803427, 1287627061, 2575254123, 5150547536, 10301096282
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Equals eigensequence of triangle A010766 and starting (1, 3, 7, 16, 33,...) = row sums of triangle A163313. - Gary W. Adamson, Jul 30 2009
The Gould & Quaintance reference, published in 2007, says that this sequence is not in the OEIS. - Olivier Gérard, Oct 20 2011
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..1000
H. W. Gould and J. Quaintance, Floor and Roof function analog of the Bell Numbers, INTEGERS, 7 (2007), #A58
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FORMULA
| a(n) is asymptotic to c*2^n where c = 0.59960731361450033896934...
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MAPLE
| with (numtheory):
a:= proc(n) option remember;
`if` (n=1, 1, add (add (a(d), d=divisors(k)), k=1..n-1))
end:
seq (a(n), n=1..40); # Alois P. Heinz, Oct 28 2011
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PROG
| (PARI) // an=vector(100); a(n)=if(n<0, 0, an[n]); // an[1]=1; for(n=2, 100, an[n]=sum(k=1, n-1, sumdiv(k, d, a(d))))
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CROSSREFS
| Cf. A010766, A163313. - Gary W. Adamson, Jul 30 2009
Sequence in context: A084631 A192968 A002936 * A182615 A054455 A178455
Adjacent sequences: A014665 A014666 A014667 * A014669 A014670 A014671
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 24 2003
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