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A333926
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The sum of recursive divisors of n.
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9
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1, 3, 4, 7, 6, 12, 8, 11, 13, 18, 12, 28, 14, 24, 24, 23, 18, 39, 20, 42, 32, 36, 24, 44, 31, 42, 31, 56, 30, 72, 32, 35, 48, 54, 48, 91, 38, 60, 56, 66, 42, 96, 44, 84, 78, 72, 48, 92, 57, 93, 72, 98, 54, 93, 72, 88, 80, 90, 60, 168, 62, 96, 104, 79, 84, 144
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OFFSET
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1,2
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COMMENTS
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The definition of recursive divisors and the number of recursive divisors of n are in A282446.
First differs from A051378 at n = 256.
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LINKS
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FORMULA
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Multiplicative with a(p^k) = 1 + Sum_{d recursive divisor of k} p^d.
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EXAMPLE
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The recursive divisors of 8 are 1, 2 and 8, therefore a(8) = 1 + 2 + 8 = 11.
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MATHEMATICA
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recDivQ[n_, 1] = True; recDivQ[n_, d_] := recDivQ[n, d] = Divisible[n, d] && AllTrue[FactorInteger[d], recDivQ[IntegerExponent[n, First[#]], Last[#]] &]; recDivs[n_] := Select[Divisors[n], recDivQ[n, #] &]; f[p_, e_] := 1 + Total[p^recDivs[e]]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100]
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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