A101299 - OEIS

A101299

Numbers n such that -1 + Sum_{x=1..n} phi(x) is a prime number.

3, 4, 6, 7, 10, 11, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 37, 38, 42, 50, 52, 53, 64, 65, 66, 70, 77, 79, 83, 91, 105, 113, 116, 126, 127, 128, 130, 132, 133, 135, 138, 141, 144, 150, 152, 157, 159, 161, 164, 168, 189, 198, 224, 225, 231, 241

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

3 = phi(1)+phi(2)+phi(3)-1 ==> 3, a prime, so 3 is a term.

5 = phi(1)+phi(2)+phi(3)+phi(4)-1 ==> 4, not a prime, so 5 is not a term.

MAPLE

with(numtheory): select(n-> isprime(add(phi(x), x=1..n)-1), [$1..300])[]; # Emeric Deutsch, Jul 20 2005

PROG

(PARI) isok(n) = isprime(sum(k=1, n, eulerphi(k))-1); \\ Michel Marcus, Aug 21 2019