OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
FORMULA
a(p) = 2 for p = primes (A000040).
a(n) = Sum_{d|n} A009194(d). - Antti Karttunen, May 09 2020
EXAMPLE
a(6) = gcd(1, sigma(1)) + gcd(2, sigma(2)) + gcd(3, sigma(3)) + gcd(6, sigma(6)) = gcd(1, 1) + gcd(2, 3) + gcd(3, 4) + gcd(6, 12) = 1 + 1 + 1 + 6 = 9.
MATHEMATICA
a[n_] := DivisorSum[n, GCD[#, DivisorSigma[1, #]] &]; Array[a, 80] (* Amiram Eldar, May 03 2020 *)
PROG
(Magma) [&+[GCD(d, &+Divisors(d)): d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = sumdiv(n, d, gcd(d, sigma(d))); \\ Michel Marcus, May 03 2020
CROSSREFS
Inverse Möbius transform of A009194.
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, May 03 2020
STATUS
approved