A180645 - OEIS

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A180645

Numbers n such that 5+phi(n)^2 is prime. Phi(n) is Euler's totient.

7, 9, 13, 14, 18, 21, 26, 28, 36, 37, 42, 57, 63, 65, 73, 74, 76, 79, 91, 95, 97, 104, 105, 108, 111, 112, 114, 117, 119, 126, 127, 130, 135, 140, 144, 146, 148, 152, 153, 156, 158, 163, 168, 180, 182, 190, 194, 195, 199, 203, 208, 210, 215, 216, 222, 224, 228

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OFFSET

1,1

COMMENTS

The sequence appears to be infinite, but I have no proof.

There are many consecutive elements in the sequence: (13,14)-(36,37)-...-(12777,12778)-...(30236,30237)-...

LINKS

Table of n, a(n) for n=1..57.

EXAMPLE

a(10)=37 since 5+phi(37)^2=1301 is a prime.

MATHEMATICA

Select[Range[250], PrimeQ[EulerPhi[#]^2+5]&] (* Harvey P. Dale, Jun 07 2011 *)