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A374784
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Denominator of the mean unitary abundancy index of the unitary divisors of n.
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5
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1, 4, 6, 8, 10, 24, 14, 16, 18, 8, 22, 16, 26, 56, 60, 32, 34, 72, 38, 80, 4, 88, 46, 96, 50, 104, 54, 112, 58, 48, 62, 64, 132, 136, 28, 16, 74, 152, 52, 160, 82, 16, 86, 176, 180, 184, 94, 64, 98, 40, 204, 208, 106, 216, 20, 224, 76, 232, 118, 160, 122, 248
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OFFSET
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1,2
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LINKS
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EXAMPLE
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For n = 4, 4 has 2 unitary divisors, 1 and 4. Their unitary abundancy indices are usigma(1)/1 = 1 and usigma(4)/4 = 5/4, and their mean unitary abundancy index is (1 + 5/4)/2 = 9/8. Therefore a(4) = denominator(9/8) = 8.
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MATHEMATICA
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f[p_, e_] := 1 + 1/(2*p^e); a[1] = 1; a[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100]
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PROG
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(PARI) a(n) = {my(f = factor(n)); denominator(prod(i = 1, #f~, 1 + 1/(2*f[i, 1]^f[i, 2]))); }
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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STATUS
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approved
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