

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
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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(n1).


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 nd > 0 then a := a+A122651r(nd, d1, 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((nd)/d), d=divisors(n) minus{1}))
end:
a:= n> `if`(n=0, 1, b(n)+b(n1));
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[n1]; Table[a[n], {n, 0, 84}] (* JeanFrançois 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((nd)\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. AdamsWatters 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



