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A332883
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If n = Product (p_j^k_j) then a(n) = denominator of Product (1 + 1/p_j^k_j).
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3
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1, 2, 3, 4, 5, 1, 7, 8, 9, 5, 11, 3, 13, 7, 5, 16, 17, 3, 19, 2, 21, 11, 23, 2, 25, 13, 27, 7, 29, 5, 31, 32, 11, 17, 35, 18, 37, 19, 39, 20, 41, 7, 43, 11, 3, 23, 47, 12, 49, 25, 17, 26, 53, 9, 55, 7, 57, 29, 59, 1, 61, 31, 63, 64, 65, 11, 67, 34, 23, 35
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OFFSET
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1,2
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COMMENTS
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Denominator of sum of reciprocals of unitary divisors of n.
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LINKS
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FORMULA
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a(n) = denominator of Sum_{d|n, gcd(d, n/d) = 1} 1/d.
a(n) = denominator of usigma(n)/n.
a(p) = p, where p is prime.
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EXAMPLE
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1, 3/2, 4/3, 5/4, 6/5, 2, 8/7, 9/8, 10/9, 9/5, 12/11, 5/3, 14/13, 12/7, 8/5, 17/16, ...
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MAPLE
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a:= n-> denom(mul(1+i[1]^i[2], i=ifactors(n)[2])/n):
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MATHEMATICA
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Table[If[n == 1, 1, Times @@ (1 + 1/#[[1]]^#[[2]] & /@ FactorInteger[n])], {n, 1, 70}] // Denominator
Table[Sum[If[GCD[d, n/d] == 1, 1/d, 0], {d, Divisors[n]}], {n, 1, 70}] // Denominator
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PROG
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(PARI) a(n) = denominator(sumdiv(n, d, if (gcd(d, n/d)==1, 1/d))); \\ Michel Marcus, Feb 28 2020
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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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