cp's OEIS Frontend

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

%I A344600 #13 May 24 2021 11:54:14
%S A344600 1,16,67,192,373,768,1111,1904,2601,3872,4651,7280,7837,11056,13215,
%T A344600 17024,18001,25488,25363,34624,37093,44576,45607,63440,60345,74368,
%U A344600 79803,96432,92653,125616,113551,144192,147297,168656,170947,220320,194581,236608,244759
%N A344600 a(n) = Sum_{k=1..n} phi(k) * (floor(n/k)^4 - floor((n-1)/k)^4).
%F A344600 Sum_{k=1..n} a(k) = A344523(n).
%F A344600 G.f.: Sum_{k >= 1} phi(k) * x^k * (1 + 11*x^k + 11*x^(2*k) + x^(3*k))/(1 - x^k)^4.
%t A344600 a[n_] := Sum[EulerPhi[k] * First @ Differences @ (Quotient[{n - 1, n}, k]^4), {k, 1, n}]; Array[a, 40] (* _Amiram Eldar_, May 24 2021 *)
%o A344600 (PARI) a(n) = sum(k=1, n, eulerphi(k)*((n\k)^4-((n-1)\k)^4));
%o A344600 (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))
%Y A344600 Cf. A344523, A344598, A344599.
%K A344600 nonn
%O A344600 1,2
%A A344600 _Seiichi Manyama_, May 24 2021