A125723 Greatest common divisor of n^6 and 6^n.

1, 4, 27, 16, 1, 46656, 1, 256, 19683, 64, 1, 2985984, 1, 64, 729, 65536, 1, 34012224, 1, 4096, 729, 64, 1, 191102976, 1, 64, 387420489, 4096, 1, 46656, 1, 1073741824, 729, 64, 1, 2176782336, 1, 64, 729, 262144, 1, 46656, 1, 4096, 531441, 64, 1, 12230590464

Offset

1,2

Comments

All terms are 3-smooth numbers (see A003586).

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = gcd(A001014(n), A000400(n)).

For n > 16, a(n) = 2^(6*A007814(n)) * 3^(6*A007949(n)).

a(A007310(n)) = 1; a(A047229(n)) > 1 for n > 0.

Example

a(6) = 6^6 = A001014(n) = A000400(n) = 46656.
a(12) = gcd(12^6, 6^12) = gcd((2^12)*(3^6), (2^12)*(3^12)) = (2^12)*(3^6)*gcd(1,3^6) = 2985984.
a(120) = gcd(120^6, 6^120) = gcd((2^18)*(3^6)*(5^6), (2^120)*(3^120)) = (2^18)*(3^6)*gcd(5^6, (2^102)*(3^114)) = 191102976.

Mathematica

Table[GCD[n^6, 6^n], {n, 50}] (* Harvey P. Dale, Sep 04 2018 *)

Prog

(PARI) A125723(n) = gcd(6^n, n^6); \\ Antti Karttunen, Feb 20 2023

Crossrefs

Cf. A001014, A000400, A003586, A007814, A007949, A007310 (positions of 1's), A047229 (of terms > 1).

Sequence in context: A351366 A365636 A345311 * A094543 A136511 A218362

Adjacent sequences: A125720 A125721 A125722 * A125724 A125725 A125726

Keyword

nonn

Author

Reinhard Zumkeller, Feb 02 2007

Status

approved