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A056855 a(n) = (Product k) * (Sum 1/k), where both the product and the sum are over those positive integers k, where k <= n and gcd(k,n) = 1. 4
1, 1, 3, 4, 50, 6, 1764, 176, 4968, 300, 10628640, 552, 1486442880, 34986, 2024400, 4098240, 70734282393600, 133542, 22376988058521600, 16294800, 121402713600, 2612325870, 4148476779335454720000, 61931424, 138951136600657920000, 1330269185700 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Since Sum_{k|n} k * Sum_{1<=m<=k, gcd(m,k)=1} 1/m = n*H(n), Sum_{k>=1} (Sum_{1<=m<=k, gcd(m,k)=1} 1/m) /k^2 = 2. - Leroy Quet, Nov 13 2004
LINKS
FORMULA
Sum_{1<=m<=n, gcd(m,n)=1} 1/m = (1/n)*Sum_{k|n} mu(n/k)*k*H(k), where H(k) = Sum_{j=1..k} 1/j. - Leroy Quet, Nov 13 2004
EXAMPLE
a(8) = 1*3*5*7*(1 + 1/3 + 1/5 + 1/7) = 176 because 1, 3, 5 and 7 are the positive integers <= 8 that are relatively prime to 8.
MAPLE
a:= n-> (l-> mul(i, i=l)*add(1/i, i=l))(
select(x-> igcd(x, n)=1, [$1..n])):
seq(a(n), n=1..40); # Alois P. Heinz, May 22 2015
MATHEMATICA
f[n_] := Block[{k = Select[Range[n], GCD[ #, n] == 1 &]}, Plus @@ (Times @@ k*Plus @@ 1/k)]; Table[ f[n], {n, 25}] (* Robert G. Wilson v, Nov 16 2004 *)
CROSSREFS
Sequence in context: A264509 A198051 A032839 * A208653 A080073 A032840
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Aug 30 2000
STATUS
approved

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Last modified February 25 07:35 EST 2024. Contains 370310 sequences. (Running on oeis4.)