

A015052


Smallest positive integer for which n divides a(n)^5.


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, 4, 65, 66, 67, 34, 69, 70, 71, 6, 73, 74, 15, 38, 77, 78
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OFFSET

1,2


COMMENTS

A multiplicative companion function n/a(n) = 1,1,1,2,1,1,1,4,3,1,1,2,1,1,1,8,1,... can be defined using the 5th instead of the 4th power in A000190, which differs from A000190 and also from A003557.  R. J. Mathar, Jul 14 2012


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Henry Bottomley, Some Smarandachetype multiplicative sequences.
Kevin A. Broughan, Restricted divisor sums, Acta Arithmetica, 101(2) (2002), 105114.
Kevin A. Broughan, Restricted divisor sums, Acta Arithmetica, 101(2) (2002), 105114.
Kevin A. Broughan, Relationship between the integer conductor and kth root functions, Int. J. Pure Appl. Math. 5(3) (2003), 253275.
Kevin A. Broughan, Relaxations of the ABC Conjecture using integer k'th roots, New Zealand J. Math. 35(2) (2006), 121136.
Henry Ibstedt, Surfing on the Ocean of Numbers, Erhus Univ. Press, Vail, 1997.
Florentin Smarandache, Collected Papers, Vol. II, Tempus Publ. Hse, Bucharest, 1996.
Eric Weisstein's World of Mathematics, Smarandache Ceil Function.


FORMULA

Multiplicative with a(p^e) = p^(ceiling(e/5)).  Christian G. Bower, May 16 2005


MATHEMATICA

f[p_, e_] := p^Ceiling[e/5]; 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]/5)); 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), A015053 (outer 6th root).
Sequence in context: A007947 A015053 A062953 * A053166 A166140 A019555
Adjacent sequences: A015049 A015050 A015051 * A015053 A015054 A015055


KEYWORD

nonn,mult,easy


AUTHOR

R. Muller


EXTENSIONS

Corrected by David W. Wilson, Jun 04 2002


STATUS

approved



