OFFSET
1,2
COMMENTS
Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n^2 except for n = 33.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.
EXAMPLE
a(5) = 15 since 15 + 5 = 20 divides phi(15)^2 + phi(5)^2 = 8^2 + 4^2 = 80.
a(33) = 1523 since 1523 + 33 = 1556 divides phi(1523)^2 + phi(33)^2 = 1522^2 + 20^2 = 2316884 = 1489*1556.
MATHEMATICA
Do[m=1; Label[aa]; If[Mod[EulerPhi[m]^2+EulerPhi[n]^2, m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]
lpim[n_]:=Module[{m=1, p2=EulerPhi[n]^2}, While[Mod[p2+EulerPhi[m]^2, m+n]!=0, m++]; m]; Array[lpim, 60] (* Harvey P. Dale, Nov 19 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Sep 29 2014
STATUS
approved