A108738 - OEIS

%I #18 Oct 26 2017 06:19:23

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

%C a(n) = n if n has no odd prime divisor, i.e. for n = 2^k (k>=0).

%H David A. Corneth, <a href="/A108738/b108738.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 a(n) = n/A078701(n).

%e a(21) = 21/3 = 7.

%p 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 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 (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 (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 Cf. A078701, A108514.

%K nonn,easy

%O 1,2

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

%E More terms from _Emeric Deutsch_ and _Reinhard Zumkeller_, Jun 24 2005