A337298 Sum of the coordinates of all relatively prime pairs of divisors of n, (d1,d2), such that d1 <= d2.

2, 5, 6, 10, 8, 21, 10, 19, 16, 29, 14, 46, 16, 37, 36, 36, 20, 61, 22, 64, 46, 53, 26, 91, 34, 61, 44, 82, 32, 141, 34, 69, 66, 77, 64, 136, 40, 85, 76, 127, 44, 181, 46, 118, 106, 101, 50, 176, 60, 133, 96, 136, 56, 173, 92, 163, 106, 125, 62, 316, 64, 133, 136, 134, 106, 261, 70

Offset

1,1

Links

Table of n, a(n) for n=1..67.

Formula

a(n) = Sum_{i|n, k|n, i<=k, gcd(i,k)=1} (i+k).

Example

a(4) = 10; There are 3 divisors of 4: {1,2,4}. If we list the relatively prime pairs (d1,d2), where d1 <= d2, we get (1,1), (1,2), (1,4). The sum of the coordinates from all pairs is 1+1+1+2+1+4 = 10.
a(5) = 8; There are 2 divisors of 5: {1,5}. The relatively prime pairs (d1,d2), where d1 <= d2 are: (1,1) and (1,5). The sum of the coordinates is then 1+1+1+5 = 8.

Mathematica

Table[Sum[Sum[(i + k) KroneckerDelta[GCD[i, k], 1] (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k}], {k, n}], {n, 100}]

Prog

(PARI) a(n) = my(d = divisors(n)); sum(i=1, #d, sum(j=1, i, if (gcd(d[i], d[j])==1, d[i]+d[j])));  \\ Michel Marcus, Aug 22 2020

Crossrefs

Cf. A018892, A337246.

Sequence in context: A054463 A295741 A007503 * A184418 A112967 A244731

Adjacent sequences: A337295 A337296 A337297 * A337299 A337300 A337301

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Aug 21 2020

Status

approved