A180647 - OEIS

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A180647

Numbers n such that 5 + phi(n)^3 is prime. Phi is Euler's totient function.

3, 4, 6, 13, 21, 26, 28, 35, 36, 39, 42, 43, 45, 49, 52, 56, 65, 67, 70, 72, 78, 79, 84, 86, 87, 90, 98, 104, 105, 112, 116, 127, 130, 134, 139, 140, 141, 144, 156, 158, 159, 168, 174, 177, 180, 188, 193, 199, 210, 212, 221, 236, 249, 254, 277, 278, 282, 291, 299

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OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

a(5) = 21 since 5 + phi(21)^3 = 5 + 12^3 = 1733 is prime.

MATHEMATICA

Select[Range[300], PrimeQ[5+EulerPhi[#]^3]&] (* Harvey P. Dale, Oct 13 2024 *)

CROSSREFS