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A348986
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Denominator of ratio sigma(n) / A325973(n), where A325973 is the arithmetic mean of {sum of squarefree divisors} and {sum of unitary divisors}.
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3
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1, 1, 1, 4, 1, 1, 1, 2, 7, 1, 1, 4, 1, 1, 1, 10, 1, 7, 1, 4, 1, 1, 1, 2, 16, 1, 2, 4, 1, 1, 1, 2, 1, 1, 1, 31, 1, 1, 1, 2, 1, 1, 1, 4, 7, 1, 1, 10, 29, 16, 1, 4, 1, 2, 1, 2, 1, 1, 1, 4, 1, 1, 7, 34, 1, 1, 1, 4, 1, 1, 1, 17, 1, 1, 16, 4, 1, 1, 1, 10, 43, 1, 1, 4, 1, 1, 1, 2, 1, 7, 1, 4, 1, 1, 1, 2, 1, 29, 7, 74, 1, 1, 1, 2, 1
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OFFSET
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1,4
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COMMENTS
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This is not multiplicative: a(4) = 4 and a(9) = 7, but a(36) = 31, not 28.
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LINKS
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FORMULA
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MATHEMATICA
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f1[p_, e_] := p + 1; f2[p_, e_] := p^e + 1; s[1] = 1; s[n_] := (Times @@ f1 @@@ (f = FactorInteger[n]) + Times @@ f2 @@@ f)/2; a[n_] := Denominator[DivisorSigma[1, n]/s[n]]; Array[a, 100] (* Amiram Eldar, Nov 06 2021 *)
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PROG
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(PARI)
A325973(n) = (1/2)*sumdiv(n, d, d*(issquarefree(d) + (1==gcd(d, n/d))));
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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