OFFSET
1,3
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(p) = 2 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.
MAPLE
g:= proc(d) option remember; igcd(numtheory:-tau(d), numtheory:-sigma(d)) end proc:
f:= n -> mul(g(d), d = numtheory:-divisors(n)):
map(f, [$1..100]); # Robert Israel, May 11 2020
MATHEMATICA
a[n_] := Product[GCD[DivisorSigma[0, d], DivisorSigma[1, d]], {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) a(n) = my(d=divisors(n)); prod(k=1, #d, gcd(numdiv(d[k]), sigma(d[k]))); \\ Michel Marcus, May 09-11 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, May 09 2020
STATUS
approved