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

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

Crossrefs

Cf. A002088.

Sequence in context: A191926 A065135 A229792 * A143837 A354005 A330172

Adjacent sequences: A101296 A101297 A101298 * A101300 A101301 A101302

Keyword

nonn,easy

Author

Jorge Coveiro, Dec 22 2004

Extensions

More terms from Emeric Deutsch, Jul 20 2005

Name edited by Michel Marcus, Aug 21 2019

Status

approved