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A122651 Number of partitions of n into distinct parts, with each part divisible by the next. 44
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
For n>0, a(n) = A167865(n) + A167865(n-1).
EXAMPLE
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].
MAPLE
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));
seq(a(n), n=0..200); # Alois P. Heinz, Mar 28 2011
MATHEMATICA
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 *)
PROG
(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 */
CROSSREFS
Sequence in context: A283303 A280079 A116513 * A343378 A351700 A361928
KEYWORD
nonn,look
AUTHOR
EXTENSIONS
More terms from R. J. Mathar, May 22 2009
a(0)=1 prepended by Max Alekseyev, Nov 13 2009
STATUS
approved

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Last modified April 17 08:35 EDT 2024. Contains 371763 sequences. (Running on oeis4.)