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A085491
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Number of ways to write n as sum of distinct divisors of n+1.
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6
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1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 5, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 5, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 31, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 26, 0, 0, 0, 0, 0, 1, 0, 6, 0, 0, 0, 23, 0, 0, 0, 1, 0, 20, 0, 0, 0, 0, 0, 21, 0, 0, 0, 1
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OFFSET
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0,12
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COMMENTS
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LINKS
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FORMULA
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a(n) = [x^n] Product_{d divides (n+1)} (1 + x^d). - Alois P. Heinz, Feb 04 2023
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EXAMPLE
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n=11, divisors of 12=11+1 that are not greater 11: {1,2,3,4,6}, 11=6+5=6+4+1, therefore a(11)=2.
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MAPLE
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a:= proc(m) option remember; local b, l; b, l:=
proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+`if`(l[i]>n, 0, b(n-l[i], i-1))))
end, sort([numtheory[divisors](m+1)[]]);
forget(b); b(m, nops(l)-1)
end:
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MATHEMATICA
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a[n_] := Module[{dd}, dd = Select[Divisors[n+1], # <= n&]; Select[ IntegerPartitions[n, dd // Length, dd], Reverse[#] == Union[#]&] // Length]; Array[a, 100, 0] (* Jean-François Alcover, Mar 12 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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