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A248568
Least positive integer m such that phi(m+n) divides m, where phi(.) is Euler's totient function.
2
1, 2, 6, 2, 20, 4, 8, 4, 12, 40, 24, 6, 20, 12, 24, 8, 48, 16, 32, 18, 24, 8, 72, 12, 44, 40, 36, 24, 132, 12, 56, 16, 60, 96, 40, 18, 180, 36, 60, 36, 144, 40, 80, 16, 72, 20, 168, 24, 92, 88, 184, 80, 276, 24, 104, 42, 48, 264, 312, 24
OFFSET
1,2
COMMENTS
Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n*(n-1) for all n > 1.
Note that for n > 1 the term a(n) should be even.
EXAMPLE
a(10) = 40 since phi(40+10) = 20 divides 40.
MATHEMATICA
Do[m=1; Label[aa]; If[Mod[m, phi[m+n]]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]
PROG
(PARI)
a(n)=m=1; while(m%eulerphi(m+n), m++); m
vector(100, n, a(n)) \\ Derek Orr, Oct 08 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Oct 08 2014
STATUS
approved