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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
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
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.
FORMULA
Multiplicative with a(p^e) = p^ceiling(e/6). - Christian G. Bower, May 16 2005
Sum_{k=1..n} a(k) ~ c * n^2, where c = (zeta(11)/2) * Product_{p prime} (1 - 1/p^2 + 1/p^3 - 1/p^4 + 1/p^5 - 1/p^6 + 1/p^7 - 1/p^8 + 1/p^9 - 1/p^10) = 0.3522558764... . - Amiram Eldar, Oct 27 2022
MATHEMATICA
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 *)
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).
Cf. A013669.
Sequence in context: A346486 A088835 A007947 * A062953 A347230 A015052
KEYWORD
nonn,mult,easy
AUTHOR
R. Muller (Research37(AT)aol.com)
EXTENSIONS
Corrected by David W. Wilson, Jun 04 2002
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)