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A280448 Sum of the GCDs of the smaller and larger parts of the partitions of 2n into two squarefree parts. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A078490 A282847 A047877 * A100692 A089640 A086659

Adjacent sequences:  A280445 A280446 A280447 * A280449 A280450 A280451

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Jan 03 2017

STATUS

approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)