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A015053
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Smallest positive integer for which n divides a(n)^6.
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9
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1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, 21, 22, 23, 6, 5, 26, 3, 14, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 10, 41, 42, 43, 22, 15, 46, 47, 6, 7, 10, 51, 26, 53, 6, 55, 14, 57, 58, 59, 30, 61, 62, 21, 2, 65, 66, 67, 34, 69, 70, 71, 6, 73, 74, 15, 38, 77, 78
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OFFSET
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1,2
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COMMENTS
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Differs from A007947 as follows: A007947(128)=2, a(128)=4; A007947(256)=2, a(256)=4; A007947(384)=6, a(384)=12; A007947(512)=2, a(512)=4; A007947(640)=10, a(640)=20, etc. - R. J. Mathar, Oct 28 2008
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
Henry Bottomley, Some Smarandache-type multiplicative sequences.
Kevin A. Broughan, Restricted divisor sums, Acta Arithmetica, 101(2) (2002), 105-114.
Kevin A. Broughan, Relationship between the integer conductor and k-th root functions, Int. J. Pure Appl. Math. 5(3) (2003), 253-275.
Kevin A. Broughan, Relaxations of the ABC Conjecture using integer k'th roots, New Zealand J. Math. 35(2) (2006), 121-136.
Henry Ibstedt, Surfing on the Ocean of Numbers, Erhus Univ. Press, Vail, 1997.
Eric Weisstein's World of Mathematics, Smarandache Ceil Function.
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FORMULA
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Multiplicative with a(p^e) = p^ceiling(e/6). - Christian G. Bower, May 16 2005
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MATHEMATICA
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spi[n_]:=Module[{k=1}, While[PowerMod[k, 6, n]!=0, k++]; k]; Array[spi, 80] (* Harvey P. Dale, Feb 29 2020 *)
f[p_, e_] := p^Ceiling[e/6]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 18 2020 *)
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PROG
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(PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i, 2] = ceil(f[i, 2]/6)); factorback(f); \\ Michel Marcus, Feb 15 2015
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CROSSREFS
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Cf. A000188 (inner square root), A019554 (outer square root), A053150 (inner 3rd root), A019555 (outer 3rd root), A053164 (inner 4th root), A053166 (outer 4th root), A015052 (5th outer root).
Sequence in context: A056554 A088835 A007947 * A062953 A015052 A053166
Adjacent sequences: A015050 A015051 A015052 * A015054 A015055 A015056
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KEYWORD
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nonn,mult,easy
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AUTHOR
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R. Muller (Research37(AT)aol.com)
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EXTENSIONS
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Corrected by David W. Wilson, Jun 04 2002
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STATUS
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approved
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