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A344524
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a(n) = Sum_{1 <= i, j, k, l, m <= n} gcd(i,j,k,l,m).
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6
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1, 33, 246, 1060, 3165, 8091, 17128, 33936, 60645, 103825, 164886, 259368, 381841, 557595, 784200, 1091056, 1462353, 1968261, 2554810, 3327120, 4230561, 5361463, 6644196, 8302020, 10113445, 12352041, 14873418, 17924356, 21225165, 25341375, 29670556, 34920348, 40625541, 47297365
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OFFSET
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1,2
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COMMENTS
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In general, for m > 2, Sum_{k=1..n} phi(k) * floor(n/k)^m ~ zeta(m-1) * n^m / zeta(m). - Vaclav Kotesovec, May 23 2021
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} phi(k) * floor(n/k)^5.
G.f.: (1/(1 - x)) * Sum_{k >= 1} phi(k) * x^k * (1 + 26*x^k + 66*x^(2*k) + 26*x^(3*k) + x^(4*k))/(1 - x^k)^5.
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MATHEMATICA
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a[n_] := Sum[EulerPhi[k] * Quotient[n, k]^5, {k, 1, n}]; Array[a, 50] (* Amiram Eldar, May 22 2021 *)
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PROG
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(PARI) a(n) = sum(i=1, n, sum(j=1, n, sum(k=1, n, sum(l=1, n, sum(m=1, n, gcd([i, j, k, l, m]))))));
(PARI) a(n) = sum(k=1, n, eulerphi(k)*(n\k)^5);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k*(1+26*x^k+66*x^(2*k)+26*x^(3*k)+x^(4*k))/(1-x^k)^5)/(1-x))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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