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A122651
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Number of partitions of n into distinct parts, with each part divisible by the next.
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44
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1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 3, 5, 5, 4, 6, 6, 4, 6, 6, 6, 9, 7, 4, 7, 8, 7, 9, 9, 6, 10, 10, 7, 10, 8, 8, 12, 9, 7, 12, 13, 8, 12, 12, 9, 16, 12, 5, 11, 13, 13, 15, 13, 9, 12, 15, 14, 17, 13, 7, 14, 14, 11, 21, 18, 13, 21, 16, 10, 14, 16, 12, 15, 15, 10, 21, 20, 13, 20, 16, 17, 25, 17, 9, 19
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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a(9) = 4 : [9], [8,1], [6,3], [6,2,1].
a(15) = 6 : [15], [14,1], [12,3], [12,2,1], [10,5], [8,4,2,1].
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MAPLE
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A122651r := proc(n, pmax, dv) option remember ; local a, d ; a := 0 ; for d in dv do if d = n and d <= pmax then a := a+1 ; elif d < pmax and n-d > 0 then a := a+A122651r(n-d, d-1, numtheory[divisors](d) minus {d} ) ; fi; od: a ; end: A122651 := proc(n) local i; A122651r(n, n, convert([seq(i, i=1..n)], set) ) ; end: for n from 1 to 120 do printf("%d, ", A122651(n)) ; od: # R. J. Mathar, May 22 2009
# second Maple program:
with(numtheory):
b:= proc(n) option remember;
`if`(n=0, 1, add(b((n-d)/d), d=divisors(n) minus{1}))
end:
a:= n-> `if`(n=0, 1, b(n)+b(n-1));
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MATHEMATICA
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b[0] = 1; b[n_] := b[n] = Sum[b[(n - d)/d], {d, Divisors[n] // Rest}]; a[0] = 1; a[n_] := b[n] + b[n-1]; Table[a[n], {n, 0, 84}] (* Jean-François Alcover, Mar 26 2013, after Alois P. Heinz *)
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PROG
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(PARI) { a(n, m=0) = local(r=0); if(n==0, return(1)); fordiv(n, d, if(d<=m, next); r+=a((n-d)\d, 1); ); r } /* Max Alekseyev */
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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