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

7,1

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

Links

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

Example

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

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}]

Prog

(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

Crossrefs

Cf. A000010, A248004, A248006, A248008.

Sequence in context: A097908 A198612 A019907 * A212194 A212162 A249445

Adjacent sequences: A248004 A248005 A248006 * A248008 A248009 A248010

Keyword

nonn

Author

Zhi-Wei Sun, Sep 29 2014

Status

approved