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Search: id:A125723
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| A125723 |
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Greatest common divisor of n^6 and 6^n. |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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)).
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EXAMPLE
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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.
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CROSSREFS
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Adjacent sequences: A125720 A125721 A125722 this_sequence A125724 A125725 A125726
Sequence in context: A132488 A144990 A102199 this_sequence A094543 A136511 A108138
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 02 2007
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