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A015053 Smallest positive integer for which n divides a(n)^6. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative with a(p^e) = p^ceiling(e/6). - Christian G. Bower, May 16 2005

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

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

H. 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.

H. Ibstedt, Surfing on the Ocean of Numbers, Erhus Univ. Press, Vail, 1997.

Eric Weisstein's World of Mathematics, Smarandache Ceil Function.

MATHEMATICA

spi[n_]:=Module[{k=1}, While[PowerMod[k, 6, n]!=0, k++]; k]; Array[spi, 80] (* Harvey P. Dale, Feb 29 2020 *)

PROG

(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

CROSSREFS

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

KEYWORD

nonn,mult

AUTHOR

R. Muller (Research37(AT)aol.com)

EXTENSIONS

Corrected by David W. Wilson, Jun 04 2002

STATUS

approved

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Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)