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A372636
a(n) = Sum_{j=1..n} Sum_{k=1..n} phi(j*k) / phi(k).
4
1, 5, 14, 31, 58, 93, 148, 219, 306, 407, 550, 695, 898, 1103, 1323, 1610, 1963, 2293, 2738, 3152, 3597, 4116, 4773, 5362, 6073, 6808, 7611, 8437, 9492, 10348, 11557, 12728, 13868, 15143, 16425, 17753, 19482, 21083, 22687, 24350, 26481, 28186, 30535, 32641
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Totient Function.
FORMULA
a(n) ~ c * n^3, where c = A330596 / 2 = 0.374267629841... . - Amiram Eldar, May 09 2024
MATHEMATICA
Table[Sum[Sum[EulerPhi[j*k], {j, 1, n}] / EulerPhi[k], {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, May 08 2024 *)
s = 1; Join[{1}, Table[s += Sum[EulerPhi[j*n] / EulerPhi[j], {j, 1, n}] + Sum[EulerPhi[j*n], {j, 1, n-1}] / EulerPhi[n], {n, 2, 50}]] (* Vaclav Kotesovec, May 08 2024 *)
PROG
(PARI) a(n) = sum(j=1, n, sum(k=1, n, eulerphi(j*k)/eulerphi(k)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 08 2024
STATUS
approved