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A320043 Row sums of the triangle A322550. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A330283

Adjacent sequences:  A320040 A320041 A320042 * A320044 A320045 A320046

KEYWORD

nonn

AUTHOR

Stefano Spezia, Dec 16 2018

STATUS

approved

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Last modified January 25 12:40 EST 2022. Contains 350572 sequences. (Running on oeis4.)