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

1,2

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

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)).

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]

Prog

(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))

Crossrefs

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

Sequence in context: A203977 A003757 A187985 * A296619 A064521 A367663

Adjacent sequences: A320040 A320041 A320042 * A320044 A320045 A320046

Keyword

nonn

Author

Stefano Spezia, Dec 16 2018

Status

approved