Search: a117180 -id:a117180
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0, 0, 0, 1, 0, 7, 1, 5, 0, 0, 3, 0, 5, 3, 7, 4, 13, 0, 23, 9, 25, 1, 2, 2, 0, 13, 1, 22, 15, 11, 0, 4, 3, 7, 19, 29, 47, 2, 21, 5, 23, 9, 25, 4, 5, 0, 27, 0, 7, 0, 8, 22, 9, 3, 7, 46, 33, 23, 11, 8, 10, 27, 79, 37, 5, 0, 10, 39, 18, 5, 5, 15, 43, 20, 61, 45, 9, 17, 14, 14, 3, 49, 19, 7, 25, 16, 16
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OFFSET
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1,6
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LINKS
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EXAMPLE
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12, the 4th nonsquarefree positive integer, is 2^2 * 3. 2^2 = 4 is the largest prime power dividing 12. 3 is the smallest prime power dividing 12. So a(4) = 4 - 3 = 1.
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MAPLE
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A013929 := proc(nmax) local a, n ; a := [] ; n :=1 ; while nops(a) < nmax do if not numtheory[issqrfree](n) then a := [op(a), n] ; fi ; n := n+1 ; od ; a ; end :
A034699 := proc(n) local ifs, res; if n = 1 then 1 ; else ifs := ifactors(n)[2] ; seq(op(1, op(i, ifs))^op(2, op(i, ifs)), i=1..nops(ifs)) ; max(%) ; fi ; end:
A034684 := proc(n) local ifs, res; if n = 1 then 1 ; else ifs := ifactors(n)[2] ; seq(op(1, op(i, ifs))^op(2, op(i, ifs)), i=1..nops(ifs)) ; min(%) ; fi ; end:
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MATHEMATICA
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s[n_] := Differences[MinMax[Power @@@ FactorInteger[n]]][[1]]; s /@ Select[Range[250], !SquareFreeQ[#] &] (* Amiram Eldar, Feb 11 2021 *)
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CROSSREFS
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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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A117181
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Highest prime-power dividing the n-th nonsquarefree positive integer.
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+10
3
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4, 8, 9, 4, 16, 9, 5, 8, 25, 27, 7, 32, 9, 8, 11, 9, 16, 49, 25, 13, 27, 8, 5, 9, 64, 17, 9, 25, 19, 16, 81, 7, 11, 9, 23, 32, 49, 11, 25, 13, 27, 16, 29, 13, 8, 121, 31, 125, 9, 128, 11, 27, 17, 7, 16, 49, 37, 25, 19, 17, 13, 32, 81, 41, 8, 169, 19, 43, 25, 16, 9, 23, 47, 27, 64, 49
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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a(n) is prime at 7, 11, ...
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LINKS
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FORMULA
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EXAMPLE
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12, the 4th nonsquarefree positive integer, is 2^2 * 3. 2^2 = 4 is the largest prime power dividing 12. So a(4) = 4.
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MAPLE
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A013929 := proc(nmax) local a, n ; a := [] ; n :=1 ; while nops(a) < nmax do if not numtheory[issqrfree](n) then a := [op(a), n] ; fi ; n := n+1 ; od ; a ; end : A034699 := proc(n) local ifs, res; if n = 1 then 1 ; else ifs := ifactors(n)[2] ; seq(op(1, op(i, ifs))^op(2, op(i, ifs)), i=1..nops(ifs)) ; max(%) ; fi ; end: a013929 := A013929(200) : for n from 1 to nops(a013929) do printf("%d, ", A034699(op(n, a013929))) ; od ; # R. J. Mathar, May 10 2007
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MATHEMATICA
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s[n_] := Max @@ Power @@@ FactorInteger[n]; s /@ Select[Range[200], !SquareFreeQ[#] &] (* Amiram Eldar, Feb 11 2021 *)
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CROSSREFS
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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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