A280448 Sum of the GCDs of the smaller and larger parts of the partitions of 2n into two squarefree parts.

1, 3, 4, 4, 6, 10, 9, 7, 6, 20, 15, 11, 17, 28, 19, 11, 23, 23, 25, 27, 36, 48, 30, 24, 12, 55, 16, 35, 39, 56, 41, 20, 55, 73, 55, 44, 50, 81, 65, 39, 53, 96, 56, 71, 33, 97, 63, 40, 29, 53, 88, 83, 71, 63, 91, 68, 98, 126, 78, 87, 80, 134, 65, 40, 107, 147, 89, 107, 119

Offset

1,2

Links

Table of n, a(n) for n=1..69.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..n} gcd(i,2n-i) * mu(i)^2 * mu(2n-i)^2, where mu is the Möbius function (A008683).

Maple

with(numtheory): A280448:=n->add(gcd(2*n-i, i)*mobius(i)^2*mobius(2*n-i)^2, i=1..n): seq(A280448(n), n=1..100);

Mathematica

Table[Sum[GCD[k, 2*n - k]*MoebiusMu[k]^2 * MoebiusMu[2*n - k]^2, {k, 1,
n}], {n, 1, 50}] (* G. C. Greubel, Jan 05 2017 *)

Prog

(PARI) for(n=1, 50, print1(sum(k=1, n, gcd(k, 2*n-k) * (moebius(k))^2 *(moebius(2*n-k))^2), ", ")) \\ G. C. Greubel, Jan 05 2017

Crossrefs

Cf. A008683, A234307, A280226.

Sequence in context: A363239 A047877 A351371 * A100692 A360724 A089640

Adjacent sequences: A280445 A280446 A280447 * A280449 A280450 A280451

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 03 2017

Status

approved