A334628 Total area of all distinct rectangles whose length and width are relatively prime and L + W = n.

0, 1, 2, 3, 10, 5, 28, 22, 42, 30, 110, 46, 182, 91, 140, 172, 408, 159, 570, 260, 420, 385, 1012, 380, 1050, 650, 1098, 770, 2030, 620, 2480, 1368, 1760, 1496, 2380, 1290, 4218, 2109, 2964, 2120, 5740, 1806, 6622, 3190, 4020, 3795, 8648, 3064, 8428, 4150, 6800, 5356, 12402

Offset

1,3

Comments

Sum of the products of the parts in each partition of n into two relatively prime parts.

Links

Table of n, a(n) for n=1..53.

Formula

a(n) = Sum_{i=1..floor(n/2)} [gcd(i,n-i) = 1] * i * (n-i), where [ ] is the Iverson bracket.

Mathematica

Table[Sum[i*(n - i) KroneckerDelta[GCD[i, n - i], 1], {i, Floor[n/2]}], {n, 60}]

Crossrefs

Cf. A023022.

Sequence in context: A328613 A064946 A078730 * A292239 A373641 A163767

Adjacent sequences: A334625 A334626 A334627 * A334629 A334630 A334631

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Sep 09 2020

Status

approved