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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

Alois P. Heinz, Table of n, a(n) for n = 0..10000

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-Fran├žois 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

Cf. A003238, A122934, A167439, A167865, A167866, A184999.

Sequence in context: A283303 A280079 A116513 * A343378 A300013 A130535

Adjacent sequences:  A122648 A122649 A122650 * A122652 A122653 A122654

KEYWORD

nonn,look

AUTHOR

Zak Seidov, Franklin T. Adams-Watters and Vladeta Jovovic, Sep 21 2006

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 October 16 09:02 EDT 2021. Contains 348041 sequences. (Running on oeis4.)