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A229997
Numerator of d(k)/d(1) + d(k-1)/d(2) + ... + d(k)/d(1), where d(1),d(2),...,d(k) are the unitary divisors of n.
4
1, 5, 10, 17, 26, 25, 50, 65, 82, 13, 122, 85, 170, 125, 52, 257, 290, 205, 362, 221, 500, 305, 530, 325, 626, 425, 730, 425, 842, 130, 962, 1025, 1220, 725, 260, 697, 1370, 905, 1700, 169, 1682, 1250, 1850, 1037, 2132, 1325, 2210, 1285, 2402, 313, 2900
OFFSET
1,2
EXAMPLE
n = 5 = 5^1 gives 5/1 + 1/5 = 26/5, so a(5) = 26;
n = 6 = (2^1)*(3^1) gives 6/1 + 3/2 + 2/3 + 1/6 = 25/3, so a(6) = 25.
The first 10 sums: 1/1, 5/2, 10/3, 17/4, 26/5, 25/3, 50/7, 65/8, 82/9, 13/1.
MATHEMATICA
r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; Table[
r[n], {n, 1, 30}]; k[n_] := Length[r[n]];
t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}]
u = Table[Plus @@ t[n], {n, 1, 60}]; Numerator[u] (* A229997 *)
Denominator[u] (* A229998 *)
CROSSREFS
Sequence in context: A105705 A061409 A342553 * A277186 A193053 A340047
KEYWORD
nonn,easy,frac
AUTHOR
Clark Kimberling, Oct 31 2013
EXTENSIONS
Definition corrected by Clark Kimberling, Jun 16 2018
STATUS
approved