A236473 Number of partitions into multiplicatively perfect numbers, cf. A007422.

1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 7, 8, 10, 10, 12, 12, 15, 17, 21, 22, 26, 27, 32, 35, 41, 44, 52, 55, 63, 68, 78, 85, 98, 105, 119, 128, 144, 156, 177, 191, 214, 231, 257, 277, 310, 335, 372, 402, 444, 478, 529, 571, 630, 681, 747, 804, 883, 951

Offset

0,7

Links

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

Example

a(10) = #{10, 8+1+1, 6+1+1+1+1, 10x1} = 4;
a(11) = #{10+1, 8+1+1+1, 6+1+1+1+1+1, 11x1} = 4;
a(12) = #{10+1+1, 8+1+1+1+1, 6+6, 6+6x1, 12x1} = 5;
a(13) = #{10+1+1+1, 8+1+1+1+1+1, 6+6+1, 6+7x1, 13x1} = 5;
a(14) = #{14, 10+1+1+1+1, 8+6, 8+6x1, 6+6+1+1, 6+8x1, 14x1} = 7;
a(15) = #{15, 14+1, 10+1+1+1+1+1, 8+6+1, 8+7x1, 6+6+1+1+1, 6+9x1, 15x1} = 8;
a(16) = #{15+1, 14+1+1, 10+6, 10+6x1, 8+8, 8+6+1+1, 8+8x1, 6+6+1+1+1+1, 6+10x1, 16x1} = 10.

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*(add(
      `if`(tau(d)=4, d, 0), d=divisors(j))+1), j=1..n)/n)
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 23 2017

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[a[n-j]*(Sum[If[DivisorSigma[0, d] == 4, d, 0], {d, Divisors[j]}] + 1), {j, 1, n}]/n];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Apr 12 2017, after Alois P. Heinz *)

Prog

(Haskell)
a236473 = p a007422_list where
   p _          0 = 1
   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

Crossrefs

Sequence in context: A027191 A122522 A227614 * A029030 A008719 A079685

Adjacent sequences: A236470 A236471 A236472 * A236474 A236475 A236476

Keyword

nonn

Author

Reinhard Zumkeller, Jan 26 2014

Status

approved