The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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-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 Cf. A003238, A122934, A167439, A167865, A167866, A184999. Sequence in context: A283303 A280079 A116513 * A343378 A351700 A361928 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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