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 A236473 Number of partitions into multiplicatively perfect numbers, cf. A007422. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 12 21:19 EDT 2021. Contains 344967 sequences. (Running on oeis4.)