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A108738 a(n) = n/(smallest odd prime divisor of n), if any.

%I A108738 #18 Oct 26 2017 06:19:23
%S A108738 1,2,1,4,1,2,1,8,3,2,1,4,1,2,5,16,1,6,1,4,7,2,1,8,5,2,9,4,1,10,1,32,
%T A108738 11,2,7,12,1,2,13,8,1,14,1,4,15,2,1,16,7,10,17,4,1,18,11,8,19,2,1,20,
%U A108738 1,2,21,64,13,22,1,4,23,14,1,24,1,2,25,4,11,26,1,16,27,2,1,28,17,2,29,8,1
%N A108738 a(n) = n/(smallest odd prime divisor of n), if any.
%C A108738 a(n) = n if n has no odd prime divisor, i.e. for n = 2^k (k>=0).
%H A108738 David A. Corneth, <a href="/A108738/b108738.txt">Table of n, a(n) for n = 1..10000</a>
%H A108738 Z. Nedev and S. Muthukrishnan, <a href="http://dimacs.rutgers.edu/TechnicalReports/abstracts/2005/2005-22.html">The Nagger-Mover Game</a>, DIMACS Tech. Report 2005-22.
%F A108738 a(n) = n/A078701(n).
%e A108738 a(21) = 21/3 = 7.
%p A108738 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 n/nn[2] else n/nn[1] fi end: seq(a(n),n=1..100); # _Emeric Deutsch_, Jun 24 2005
%t A108738 f[n_] := If[IntegerQ@Log[2, n], n, pf = First /@ FactorInteger@n; If[ EvenQ@n, n/pf[[2]], n/pf[[1]] ]]; Array[f, 89] (* _Robert G. Wilson v_, Sep 02 2006 *)
%o A108738 (PARI) a(n) = my(v = select(x->((x%2)==1), factor(n)[,1]));  n/if (#v, vecmin(v), 1); \\ _Michel Marcus_, Oct 25 2017
%o A108738 (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]\=p))); res} \\ _David A. Corneth_, Oct 25 2017
%Y A108738 Cf. A078701, A108514.
%K A108738 nonn,easy
%O A108738 1,2
%A A108738 S. Muthukrishnan (muthu(AT)research.att.com), Jun 23 2005
%E A108738 More terms from _Emeric Deutsch_ and _Reinhard Zumkeller_, Jun 24 2005