|
|
A275254
|
|
The bi-unitary gcd-sum function.
|
|
2
|
|
|
1, 3, 5, 7, 9, 14, 13, 15, 17, 25, 21, 30, 25, 36, 43, 31, 33, 47, 37, 57, 61, 58, 45, 64, 49, 69, 53, 82, 57, 108, 61, 63, 99, 91, 113, 99, 73, 102, 117, 117, 81, 163, 85, 132, 141, 124, 93, 130, 97, 135, 155, 157, 105, 146, 181
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Sum_{k=1..n} a(k) = c * n^2 * log(n) / 2 + O(n^2), where c = Product_{p prime} (1 - (3*p-1)/(p^2*(p+1))) = zeta(2) * Product_{p prime} (1 - (2*p-1)^2/p^4) = A013661 * A256392 = 0.35823163000196141456... . - Amiram Eldar, Dec 22 2023
|
|
MAPLE
|
Pstarstar := proc(n)
end proc:
|
|
MATHEMATICA
|
phi[x_, n_] := Sum[Boole[GCD[k, n] == 1], {k, 1, x}]; uphi[1]=1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); a[n_] := DivisorSum[n, uphi[#] * phi[n/#, #] &, GCD[#, n/#] == 1 &]; Array[a, 100] (* Amiram Eldar, Sep 09 2019 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|