

A108514


If n is a power of 2, a(n)=n; otherwise a(n) = (p1)*n/p where p = smallest odd prime divisor of n.


4



1, 2, 2, 4, 4, 4, 6, 8, 6, 8, 10, 8, 12, 12, 10, 16, 16, 12, 18, 16, 14, 20, 22, 16, 20, 24, 18, 24, 28, 20, 30, 32, 22, 32, 28, 24, 36, 36, 26, 32, 40, 28, 42, 40, 30, 44, 46, 32, 42, 40, 34, 48, 52, 36, 44, 48, 38, 56, 58, 40, 60, 60, 42, 64, 52, 44, 66, 64, 46, 56, 70, 48, 72, 72, 50
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OFFSET

1,2


LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000
Z. Nedev, A Reduced Computational Complexity Strategy for the MagnusDerek Game, International Mathematical Forum, Vol. 9, 2014, no. 7, pp. 325  333. See p. 326.
Z. Nedev and S. Muthukrishnan, The NaggerMover Game, DIMACS Tech. Report 200522.


MAPLE

with(numtheory): a:=proc(n) local nn: nn:=factorset(n): if n=1 then 1 elif nn={2} then n elif nn[1]=2 then (nn[2]1)*n/nn[2] else (nn[1]1)*n/nn[1] fi end:


MATHEMATICA

Array[If[IntegerQ@ Log2@ #1, #1, #1 (#2  1)/#2] & @@ {#, SelectFirst[FactorInteger[#][[All, 1]], # > 2 &]} &, 75] (* Michael De Vlieger, Oct 25 2017 *)


PROG

(PARI) first(n) = {my(res = vector(n, i, i)); forprime(p = 3, n, for(k = 1, n\p, if(res[k*p] == k*p, res[k*p]*=(p1)/p))); res} \\ David A. Corneth, Oct 25 2017


CROSSREFS

Cf. A108738.
Sequence in context: A035114 A202103 A062570 * A120456 A115383 A219156
Adjacent sequences: A108511 A108512 A108513 * A108515 A108516 A108517


KEYWORD

nonn


AUTHOR

S. Muthukrishnan (muthu(AT)research.att.com), Jun 23 2005


EXTENSIONS

Definition revised by N. J. A. Sloane, Oct 28 2017 at the suggestion of Michel Marcus.


STATUS

approved



