A344600 a(n) = Sum_{k=1..n} phi(k) * (floor(n/k)^4 - floor((n-1)/k)^4).

1, 16, 67, 192, 373, 768, 1111, 1904, 2601, 3872, 4651, 7280, 7837, 11056, 13215, 17024, 18001, 25488, 25363, 34624, 37093, 44576, 45607, 63440, 60345, 74368, 79803, 96432, 92653, 125616, 113551, 144192, 147297, 168656, 170947, 220320, 194581, 236608, 244759

Offset

1,2

Links

Table of n, a(n) for n=1..39.

Formula

Sum_{k=1..n} a(k) = A344523(n).

G.f.: Sum_{k >= 1} phi(k) * x^k * (1 + 11*x^k + 11*x^(2*k) + x^(3*k))/(1 - x^k)^4.

Mathematica

a[n_] := Sum[EulerPhi[k] * First @ Differences @ (Quotient[{n - 1, n}, k]^4), {k, 1, n}]; Array[a, 40] (* Amiram Eldar, May 24 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, eulerphi(k)*((n\k)^4-((n-1)\k)^4));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k*(1+11*x^k+11*x^(2*k)+x^(3*k))/(1-x^k)^4))

Crossrefs

Cf. A344523, A344598, A344599.

Sequence in context: A216306 A321180 A100186 * A271913 A178574 A005906

Adjacent sequences: A344597 A344598 A344599 * A344601 A344602 A344603

Keyword

nonn

Author

Seiichi Manyama, May 24 2021

Status

approved