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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 (list; graph; refs; listen; history; text; internal format)
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}]

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

Zhi-Wei Sun, Sep 29 2014

STATUS

approved

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Last modified May 28 15:55 EDT 2020. Contains 334684 sequences. (Running on oeis4.)