A248030 Least positive integer m such that m + n divides sigma(m)*phi(n), where sigma(.) and phi(.) are given by A000203 and A000010.

2, 12, 4, 2, 3, 6, 2, 10, 3, 2, 21, 8, 3, 22, 13, 8, 9, 6, 8, 12, 3, 8, 10, 4, 5, 10, 21, 8, 20, 26, 4, 8, 7, 14, 13, 12, 8, 4, 33, 8, 23, 6, 20, 12, 3, 16, 22, 72, 7, 10, 13, 4, 27, 42, 5, 24, 15, 26, 57, 18, 11, 38, 27, 20, 31, 4, 21, 36, 19, 2

Offset: 1

Author

Zhi-Wei Sun, Sep 29 2014

Keywords

• nonn

Comments

Conjecture: a(n) < 2*n for any n > 2.

Numbers n such that a(n) > n: 1, 2, 3, 8, 11, 14, 48, 227, 908, 4478, ... The next number, if it exists, is greater than 10^5. - Derek Orr, Sep 29 2014

Examples

			a(2) = 12 since 12 + 2 = 14 divides sigma(12)*phi(2) = 28.
		

Links

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

Crossrefs

Cf. A000010, A000203, A248004, A248007, A248008, A248029.

Programs

Mathematica

Do[m=1;Label[aa];If[Mod[DivisorSigma[1,m]*EulerPhi[n],m+n]==0,Print[n," ",m];Goto[bb]];m= m+1; Goto[aa];Label[bb];Continue,{n,1,70}]
lpim[n_]:=Module[{m=1,ephn=EulerPhi[n]},While[Mod[ephn*DivisorSigma[1,m],m+n]!=0, m++]; m]; Array[lpim,70] (* Harvey P. Dale, Feb 14 2024 *)

PARI

a(n)=m=1;while((eulerphi(n)*sigma(m))%(m+n),m++);m
vector(100,n,a(n)) \\ Derek Orr, Sep 29 2014