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A174113
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Smallest number k such that k, k+1, and k+2 are all divisible by an n-th power.
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4
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48, 1375, 33614, 2590623, 26890623, 2372890624, 70925781248, 2889212890624, 61938212890624, 4497636425781248, 8555081787109375, 2665760081787109375, 98325140081787109375, 198816740081787109374, 11776267480163574218750, 872710687480163574218750, 50783354512519836425781248
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OFFSET
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2,1
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COMMENTS
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Least of the smallest trio of consecutive numbers divisible by an n-th power.
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 1375, p. 135, Ellipses, Paris 2008.
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LINKS
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FORMULA
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EXAMPLE
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a(3) = 1375 because
1375 = 11 * 5^3;
1376 = 172 * 2^3;
1377 = 51 * 3^3.
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MAPLE
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with(numtheory):for n from 2 to 6 do: i:=0:for k from 1 to 3000000 while(i=0) do:j:=0:
for a from 0 to 2 do: ii:=0:for m from 1 to 4 while(ii=0) do:p:=ithprime(m)^n:if irem(k+a, p)=0 then j:=j+1:ii:=1:else fi:od:od:if j=3 then i:=1:print(k):else fi:od:od:
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PROG
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(PARI) a(n)=my(ch, t, best=30^n); forprime(a=2, 29, forprime(b=2, 29, if(a==b, next); ch=chinese(Mod(0, a^n), Mod(-1, b^n)); if(lift(ch)>=best, next); forprime(c=2, 29, if(a==c || b==c, next); t=lift(chinese(ch, Mod(-2, c^n))); if(t<best, best=t)))); best \\ Charles R Greathouse IV, Jan 16 2012
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CROSSREFS
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Cf. A068780, A068781, A068140, A068782, A068783, A068784, A045330, A059737, A063528, A051903, A051903.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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