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

1,2

Comments

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

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.

Formula

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

Example

a(21) = 21/3 = 7.

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 *)

Prog

(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

Crossrefs

Cf. A078701, A108514.

Sequence in context: A325566 A218621 A079891 * A064405 A235872 A100762

Adjacent sequences: A108735 A108736 A108737 * A108739 A108740 A108741

Keyword

nonn,easy

Author

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

Extensions

More terms from Emeric Deutsch and Reinhard Zumkeller, Jun 24 2005

Status

approved