A108738 a(n) = n/(smallest odd prime divisor of n), if any.
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, 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, 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
Offset: 1
Examples
a(21) = 21/3 = 7.
Links
- David A. Corneth, Table of n, a(n) for n = 1..10000
- Z. Nedev and S. Muthukrishnan, The Nagger-Mover Game, DIMACS Tech. Report 2005-22.
Programs
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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 n/nn[2] else n/nn[1] fi end: seq(a(n),n=1..100); # Emeric Deutsch, Jun 24 2005 -
Mathematica
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 *)
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PARI
a(n) = my(v = select(x->((x%2)==1), factor(n)[,1])); n/if (#v, vecmin(v), 1); \\ Michel Marcus, Oct 25 2017
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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
Formula
a(n) = n/A078701(n).
Extensions
More terms from Emeric Deutsch and Reinhard Zumkeller, Jun 24 2005
Comments