This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 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. 5
 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 * A300013 A130535 A329194 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)