OFFSET
1,2
COMMENTS
Inverse Möbius transform of A009205. - Antti Karttunen, May 19 2020
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) = 3 for p = odd primes (A065091).
EXAMPLE
a(6) = gcd(tau(1), sigma(1)) + gcd(tau(2), sigma(2)) + gcd(tau(3), sigma(3)) + gcd(tau(6), sigma(6)) = gcd(1, 1) + gcd(2, 3) + gcd(2, 4) + gcd(4, 12) = 1 + 1 + 2 + 4 = 8.
MATHEMATICA
a[n_] := DivisorSum[n, GCD[DivisorSigma[0, #], DivisorSigma[1, #]] &]; Array[a, 100] (* Amiram Eldar, May 07 2020 *)
PROG
(Magma) [&+[GCD(#Divisors(d), &+Divisors(d)): d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = sumdiv(n, d, gcd(numdiv(d), sigma(d))); \\ Michel Marcus, May 07 2020
CROSSREFS
Cf. A334729 (with product, instead of sum).
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, May 06 2020
STATUS
approved