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A337323
a(n) = gcd(n, tau(n), sigma(n), pod(n)) where tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisors of k (A000203) and pod(k) is the product of divisors of k (A007955).
5
1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1
OFFSET
1,6
COMMENTS
GCD(n, tau(n), sigma(n), pod(n)) = GCD(n, tau(n), sigma(n)). - David A. Corneth, Aug 24 2020
LINKS
FORMULA
a(p) = 1 for p = primes (A000040).
a(n) = 1 for n = p^k, p prime, k >= 0 (A000961). - Bernard Schott, Apr 01 2021
EXAMPLE
a(6) = gcd(6, tau(6), sigma(6), pod(6)) = gcd(6, 4, 12, 36) = 2.
MAPLE
f:= proc(n) uses numtheory; igcd(n, tau(n), sigma(n)) end proc:
map(f, [$1..100]); # Robert Israel, Sep 01 2020
MATHEMATICA
a[n_] := GCD @@ {n, DivisorSigma[0, n], DivisorSigma[1, n]}; Array[a, 100] (* Amiram Eldar, Aug 24 2020 *)
PROG
(Magma) [GCD([n, #Divisors(n), &+Divisors(n), &*Divisors(n)]): n in [1..100]]
(PARI) a(n) = my(f=factor(n)); gcd([n, sigma(f), numdiv(f)]); \\ Michel Marcus, Apr 01 2021
CROSSREFS
Cf. A336722 (gcd(tau(n), sigma(n), pod(n))).
Cf. A337324 (least m such that gcd(m, tau(m), sigma(m), pod(m)) = n).
Cf. A336723 (lcm(tau(n), sigma(n), pod(n))) = (lcm(n, tau(n), sigma(n), pod(n))).
Sequence in context: A348928 A124766 A359233 * A344770 A293895 A375120
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, Aug 23 2020
STATUS
approved