OFFSET
1,6
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
FORMULA
a(p) = 1 for p = primes (A000040).
EXAMPLE
a(6) = gcd(sigma(1), pod(1)) * gcd(sigma(2), pod(2)) * gcd(sigma(3), pod(3)) * gcd(sigma(6), pod(6)) = gcd(1, 1) * gcd(3, 2) * gcd(4, 3) * gcd(12, 36) = 1 * 1 * 1 * 12 = 12.
MATHEMATICA
a[n_] := Product[GCD[DivisorSigma[1, d], d^(DivisorSigma[0, d]/2)], {d, Divisors[n]}]; Array[a, 100] (* Amiram Eldar, May 09 2020 *)
PROG
(Magma) [&*[GCD(&+Divisors(d), &*Divisors(d)): d in Divisors(n)]: n in [1..100]]
(PARI) pod(n) = vecprod(divisors(n));
a(n) = my(d=divisors(n)); prod(k=1, #d, gcd(sigma(d[k]), pod(d[k]))); \\ Michel Marcus, May 09-11 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, May 09 2020
STATUS
approved