A248007 Least positive integer m such that m + n divides phi(m)*phi(n), where phi(.) is Euler's totient function.

5, 8, 3, 14, 9, 20, 11, 10, 9, 16, 7, 18, 5, 12, 3, 38, 21, 8, 15, 58, 9, 20, 11, 18, 14, 32, 7, 14, 13, 12, 35, 22, 9, 24, 7, 46, 13, 31, 3, 42, 45, 16, 11, 30, 13, 44, 19, 27, 25, 40, 15, 26, 28, 36, 35, 28, 9, 64, 7, 54, 21, 28, 19, 26

Offset: 7

Author

Zhi-Wei Sun, Sep 29 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for any n > 6. - Zhi-Wei Sun, Sep 29 2014

Numbers n for which a(n) > n: 10, 12, 22, 26, 42, 78, 166, 266, 290. The next term in this mini-sequence, if it exists, is greater than 3*10^4. I conjecture this list is finite. - Derek Orr, Sep 29 2014

a(2^n) <= 2^n for all n > 2. Also, if a(i) = j, then a(j) <= i. - Derek Orr, Sep 29 2014

Examples

			a(10) = 14 since 10 + 14 divides phi(10)*phi(14) = 4*6 = 24.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 7..10000

Crossrefs

Cf. A000010, A248004, A248006, A248008.

Programs

Mathematica

Do[m=1; Label[aa]; If[Mod[EulerPhi[m]*EulerPhi[n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 7, 70}]

PARI

a(n)=m=1;while((eulerphi(m)*eulerphi(n))%(m+n),m++);m
vector(100,n,a(n+6)) \\ Derek Orr, Sep 29 2014