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

Author

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

Keywords

• nonn
• easy

Comments

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

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.

Crossrefs

Cf. A078701, A108514.

Programs

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 *)

PARI

a(n) = my(v = select(x->((x%2)==1), factor(n)[,1]));  n/if (#v, vecmin(v), 1); \\ Michel Marcus, Oct 25 2017

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