OFFSET
1,1
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Aug 21 2020
STATUS
approved