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A344599
a(n) = Sum_{k=1..n} phi(k) * (floor(n/k)^3 - floor((n-1)/k)^3).
2
1, 8, 21, 46, 65, 126, 133, 224, 261, 364, 341, 618, 481, 722, 837, 1000, 833, 1404, 1045, 1718, 1641, 1798, 1541, 2760, 2065, 2516, 2673, 3346, 2465, 4410, 2821, 4256, 4041, 4312, 4469, 6462, 4033, 5390, 5637, 7504, 4961, 8532, 5461, 8186, 8613, 7906, 6533, 11736, 7861, 10640, 9621
OFFSET
1,2
FORMULA
Sum_{k=1..n} a(k) = A344522(n).
G.f.: Sum_{k >= 1} phi(k) * x^k * (1 + 4*x^k + x^(2*k))/(1 - x^k)^3.
MATHEMATICA
a[n_] := Sum[EulerPhi[k] * First @ Differences @ (Quotient[{n - 1, n}, k]^3), {k, 1, n}]; Array[a, 40] (* Amiram Eldar, May 24 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, eulerphi(k)*((n\k)^3-((n-1)\k)^3));
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k*(1+4*x^k+x^(2*k))/(1-x^k)^3))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 24 2021
STATUS
approved