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A336722 a(n) = gcd(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). 7
1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 3, 1, 2, 1, 4, 1, 4, 1, 2, 1, 2, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 8, 1, 2, 3, 4, 1, 2, 1, 1, 1, 2, 1, 8, 1, 8, 1, 2, 1, 12, 1, 4, 1, 1, 1, 8, 1, 2, 1, 8, 1, 3, 1, 2, 1, 2, 1, 8, 1, 2, 1, 2, 1, 4, 1, 4, 1, 4, 1, 6, 1, 2, 1, 4, 1, 12, 1, 1, 3, 1, 1, 8, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

a(n) = tau(n) for numbers n: 1, 6, 14, 22, 30, 38, 42, 46, 54, 56, 60, 62, 66, 70, 78, 86, 94, 96, 102, ...

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(p) = 1 for p = primes (A000040).

a(n) = gcd(A007955(n), A009205(n)). - Antti Karttunen, Aug 10 2020

EXAMPLE

a(6) = gcd(tau(6), sigma(6), pod(6)) = gcd(4, 12, 36) = 4.

MATHEMATICA

a[n_] := GCD @@ {(d = DivisorSigma[0, n]), DivisorSigma[1, n], n^(d/2)}; Array[a, 100] (* Amiram Eldar, Aug 01 2020 *)

PROG

(MAGMA) [GCD([#Divisors(n), &+Divisors(n), &*Divisors(n)]): n in [1..100]]

(PARI)

A007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)); \\ From A007955

A336722(n) = gcd(A007955(n), gcd(numdiv(n), sigma(n))); \\ Antti Karttunen, Aug 10 2020

CROSSREFS

Cf. A009205 (gcd(tau(n), sigma(n)), A306671 (gcd(tau(n), pod(n)), A306682 (gcd(sigma(n), pod(n)).

Cf. A000005 (tau(n)), A000203 (sigma(n)), A007955 (pod(n)), A336723 (lcm(tau(n), sigma(n), pod(n))).

Cf. A277521 (numbers k such that a(k) = tau(k) and simultaneously A336723(k) = pod(k)).

Sequence in context: A229293 A269443 A039927 * A073802 A132157 A103163

Adjacent sequences:  A336719 A336720 A336721 * A336723 A336724 A336725

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Aug 01 2020

EXTENSIONS

Data section extended up to a(105) by Antti Karttunen, Aug 10 2020

STATUS

approved

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Last modified June 23 06:51 EDT 2021. Contains 345395 sequences. (Running on oeis4.)