A320043 Row sums of the triangle A322550.

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

Offset: 1

Author

Stefano Spezia, Dec 16 2018

Keywords

• nonn

Comments

Conjecture: a(n) is not a perfect square except for n = 1, 6 and 96.

Links

• Stefano Spezia, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000027, A000290, A000578, A050873, A322550.

Programs

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]];

Maple

a := n -> sum((n+1-k)^2*k/gcd(n+1-k, k)^3, k = 1 .. n): seq(a(n), n = 1 .. 50);

Mathematica

a[n_]:=Sum[(n+1-k)^2*k/GCD[n+1-k,k]^3, {k, 1, n}]; Array[a, 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))

Formula

a(n) = Sum_{k=1..n} (n + 1 - k)^2*k/gcd(n + 1 - k, k)^3.

a(n) = Sum_{k=1..n} A000290(n + 1 - k)*A000027(k)/A000578(A050873(n + 1 - k, k)).