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1, 4, 3, 13, 4, 2, 3, 8, 31, 16, 7, 39, 9, 2, 2, 121, 10, 124, 6, 52, 9, 14, 5, 4, 57, 12, 39, 39, 16, 8, 19, 52, 7, 40, 2, 31, 21, 8, 27, 32, 22, 3, 12, 13, 124, 5, 9, 363, 7, 76, 5, 117, 10, 26, 14, 4, 9, 64, 31, 26, 34, 19, 93, 1093, 12, 7, 18, 130, 15, 8, 37, 248, 40, 28, 171, 78, 7, 18, 21, 484, 71, 88, 15, 117
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OFFSET
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1,2
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COMMENTS
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Numerator of ratio A003973(n) / A000203(n). This sequence gives the numerators when presented in its lowest terms, while A355934 gives the denominators. As both A000203 and A003973 are multiplicative sequences, their ratio is also: 1, 4/3, 3/2, 13/7, 4/3, 2/1, 3/2, 8/3, 31/13, 16/9, 7/6, 39/14, 9/7, 2/1, 2/1, 121/31, 10/9, 124/39, 6/5, etc.
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LINKS
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FORMULA
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MATHEMATICA
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f[p_, e_] := ((q = NextPrime[p])^(e + 1) - 1)/(q - 1); a[1] = 1; a[n_] := Numerator[Times @@ f @@@ FactorInteger[n] / DivisorSigma[1, n]]; Array[a, 100] (* Amiram Eldar, Jul 22 2022 *)
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PROG
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(PARI)
A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
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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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