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A320043
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Row sums of the triangle A322550.
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2
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1, 6, 13, 50, 37, 196, 189, 384, 351, 1210, 601, 2366, 1471, 2156, 2941, 6936, 3277, 10830, 5563, 9022, 9681, 23276, 9897, 26300, 19267, 30030, 23043, 58870, 21087, 76880, 46717, 59296, 57801, 83546, 50281, 156066, 90973, 117968, 90539, 235340, 86179, 284746
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OFFSET
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1,2
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COMMENTS
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Conjecture: a(n) is not a perfect square except for n = 1, 6 and 96.
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} (n + 1 - k)^2*k/gcd(n + 1 - k, k)^3.
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MAPLE
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a := n -> sum((n+1-k)^2*k/gcd(n+1-k, k)^3, k = 1 .. n): seq(a(n), n = 1 .. 50);
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MATHEMATICA
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a[n_]:=Sum[(n+1-k)^2*k/GCD[n+1-k, k]^3, {k, 1, n}]; Array[a, 50]
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PROG
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(GAP) List([1..50], n->Sum([1..n], k->(n+1-k)^2*k/GcdInt(n+1-k, k)^3));
(Magma) [(&+[(n+1-k)^2*k/Gcd(n+1-k, k)^3: k in [1..n]]): n in [1..50]];
(Maxima) a(n):=sum((n+1-k)^2*k/gcd(n+1-k, k)^3, k, 1, n)$ makelist(a(n), n, 1, 50);
(PARI)
a(n) = sum(k=1, n, (n+1-k)^2*k/gcd(n+1-k, k)^3);
vector(50, n, a(n))
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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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