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Search: id:A117180
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| A117180 |
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Lowest prime-power dividing n-th non-squarefree positive integer. |
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+0
3
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| 4, 8, 9, 3, 16, 2, 4, 3, 25, 27, 4, 32, 4, 5, 4, 5, 3, 49, 2, 4, 2, 7, 3, 7, 64, 4, 8, 3, 4, 5, 81, 3, 8, 2, 4, 3, 2, 9, 4, 8, 4, 7, 4, 9, 3, 121, 4, 125, 2, 128, 3, 5, 8, 4, 9, 3, 4, 2, 8, 9, 3, 5, 2, 4, 3, 169, 9, 4, 7, 11, 4, 8, 4, 7, 3, 4, 2, 8, 3, 9, 13, 4, 8, 4, 7, 9, 3, 8, 2, 4, 3, 2, 243, 4, 5, 8
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) is prime at 4,6,8,...
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FORMULA
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a(n) = A034684(A013929(n)).
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EXAMPLE
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12, the 4th non-squarefree positive integer, is 2^2 * 3. 3 is the smallest prime power dividing 12. So a(4)= 3.
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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 : A034684 := proc(n) local ifs; 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: a013929 := A013929(200) : for n from 1 to nops(a013929) do printf("%d, ", A034684(op(n, a013929))) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 10 2007
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CROSSREFS
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Cf. A034684, A013929, A117181, A117182.
Sequence in context: A096872 A123959 A096412 this_sequence A123531 A117181 A108616
Adjacent sequences: A117177 A117178 A117179 this_sequence A117181 A117182 A117183
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Mar 01 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 10 2007
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