A108514 If n is a power of 2, a(n)=n; otherwise a(n) = (p-1)*n/p where p = smallest odd prime divisor of n.

1, 2, 2, 4, 4, 4, 6, 8, 6, 8, 10, 8, 12, 12, 10, 16, 16, 12, 18, 16, 14, 20, 22, 16, 20, 24, 18, 24, 28, 20, 30, 32, 22, 32, 28, 24, 36, 36, 26, 32, 40, 28, 42, 40, 30, 44, 46, 32, 42, 40, 34, 48, 52, 36, 44, 48, 38, 56, 58, 40, 60, 60, 42, 64, 52, 44, 66, 64, 46, 56, 70, 48, 72, 72, 50

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Z. Nedev, A Reduced Computational Complexity Strategy for the Magnus-Derek Game, International Mathematical Forum, Vol. 9, 2014, no. 7, pp. 325 - 333. See p. 326.

Z. Nedev and S. Muthukrishnan, The Nagger-Mover Game, DIMACS Tech. Report 2005-22.

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 (nn[2]-1)*n/nn[2] else (nn[1]-1)*n/nn[1] fi end:

Mathematica

Array[If[IntegerQ@ Log2@ #1, #1, #1 (#2 - 1)/#2] & @@ {#, SelectFirst[FactorInteger[#][[All, 1]], # > 2 &]} &, 75] (* Michael De Vlieger, Oct 25 2017 *)

Prog

(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-1)/p))); res} \\ David A. Corneth, Oct 25 2017

Crossrefs

Cf. A108738.

Sequence in context: A202103 A333787 A062570 * A317419 A364843 A372678

Adjacent sequences: A108511 A108512 A108513 * A108515 A108516 A108517

Keyword

nonn

Author

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

Extensions

Definition revised by N. J. A. Sloane, Oct 28 2017 at the suggestion of Michel Marcus.

Status

approved