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Search: id:A117181
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| A117181 |
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Highest prime-power dividing n-th non-squarefree positive integer. |
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+0
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
(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 7,11,...
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FORMULA
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a(n) = A034699(A013929(n)).
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EXAMPLE
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12, the 4th non-squarefree 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 (mathar(AT)strw.leidenuniv.nl), May 10 2007
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CROSSREFS
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Cf. A034699, A013929, A117180, A117182.
Sequence in context: A096412 A117180 A123531 this_sequence A108616 A010480 A127162
Adjacent sequences: A117178 A117179 A117180 this_sequence A117182 A117183 A117184
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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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