A248007 - OEIS

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

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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