

A248035


Least positive integer m such that m + n divides phi(m)^2 + phi(n)^2, where phi(.) is Euler's totient function.


4



1, 3, 2, 1, 15, 14, 3, 8, 9, 30, 30, 14, 7, 6, 5, 9, 3, 8, 55, 60, 9, 4, 83, 28, 25, 71, 9, 1, 24, 4, 43, 32, 1523, 30, 13, 9, 35, 3, 21, 24, 17, 18, 7, 8, 99, 166, 5, 4, 3, 32, 205, 6, 36, 18, 19, 19, 40, 78, 9, 8
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OFFSET

1,2


COMMENTS

Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n^2 except for n = 33.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000
ZhiWei Sun, A new theorem on the primecounting 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

Cf. A000010, A247975, A248007, A248036.
Sequence in context: A136217 A166884 A136220 * A088956 A106208 A129377
Adjacent sequences: A248032 A248033 A248034 * A248036 A248037 A248038


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Sep 29 2014


STATUS

approved



