A248568 Least positive integer m such that phi(m+n) divides m, where phi(.) is Euler's totient function.

1, 2, 6, 2, 20, 4, 8, 4, 12, 40, 24, 6, 20, 12, 24, 8, 48, 16, 32, 18, 24, 8, 72, 12, 44, 40, 36, 24, 132, 12, 56, 16, 60, 96, 40, 18, 180, 36, 60, 36, 144, 40, 80, 16, 72, 20, 168, 24, 92, 88, 184, 80, 276, 24, 104, 42, 48, 264, 312, 24

Offset: 1

Author

Zhi-Wei Sun, Oct 08 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n*(n-1) for all n > 1.

Note that for n > 1 the term a(n) should be even.

Examples

			a(10) = 40 since phi(40+10) = 20 divides 40.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A248007, A248058.

Programs

Mathematica

Do[m=1;Label[aa];If[Mod[m,phi[m+n]]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]

PARI

a(n)=m=1;while(m%eulerphi(m+n),m++);m
vector(100,n,a(n)) \\ Derek Orr, Oct 08 2014