

A229998


Denominator of sum{p(i(k+1j))^e(i(k+1j))/p(i(j))^e(i(j)), j = 1..k}, where p(i(1))^e(i(1))*...*p(i(k))^e(i(k)) is the prime factorization of n.


2



1, 2, 3, 4, 5, 3, 7, 8, 9, 1, 11, 6, 13, 7, 3, 16, 17, 9, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 3, 31, 32, 33, 17, 7, 18, 37, 19, 39, 4, 41, 21, 43, 22, 45, 23, 47, 24, 49, 5, 51, 26, 53, 27, 55, 28, 57, 29, 59, 3, 61, 31, 63, 64, 1, 33, 67, 2, 69, 7
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..70.


EXAMPLE

n = 5 = 5^1 gives 5/1 + 1/5 = 26/5, so a(5) = 5;
n = 6 = (2^1)*(3^1) gives 6/1 + 3/2 + 2/3 + 1/6 = 25/3, so a(6) = 3.
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

Cf. A229997.
Sequence in context: A274690 A081810 A071829 * A067620 A294650 A053585
Adjacent sequences: A229995 A229996 A229997 * A229999 A230000 A230001


KEYWORD

nonn,easy,frac


AUTHOR

Clark Kimberling, Oct 31 2013


STATUS

approved



