

A248007


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


8



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.  ZhiWei 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 minisequence, 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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



