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A125723 Greatest common divisor of n^6 and 6^n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All terms are 3-smooth numbers (see A003586), for n>16: a(n)=2^(6*A007814(n))*3^(6*A007949(n));

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

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

LINKS

Table of n, a(n) for n=1..48.

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 *)

CROSSREFS

Sequence in context: A320626 A144990 A102199 * A094543 A136511 A218362

Adjacent sequences:  A125720 A125721 A125722 * A125724 A125725 A125726

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 02 2007

STATUS

approved

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Last modified October 29 12:00 EDT 2020. Contains 338066 sequences. (Running on oeis4.)