A039689 -id:A039689 - cp's OEIS frontend

A039698 Numbers k such that phi(k) + 1 is prime.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 21, 22, 23, 26, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 41, 42, 43, 46, 47, 48, 49, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 67, 71, 73, 74, 75, 76, 77, 79, 82, 83, 86, 88, 89, 91, 93, 94, 95, 97, 98, 99, 100, 101, 103

Offset: 1

Olivier Gérard

Positive integers k for which values of A039649(k) are primes. - Vladimir Shevelev, May 10 2008
For every prime p, the numbers p and 2p are terms of this sequence. - Vladimir Shevelev, May 10 2008
Union of A000040 and A066071. - Ray Chandler, May 26 2008

			phi(10)+1 = 4+1 = 5, a prime number, so 10 is a term.

Antti Karttunen, Table of n, a(n) for n = 1..26197 (first 1000 terms from Vincenzo Librandi)

Cf. A000010, A000040, A006093, A039649, A066071, A007614.
Cf. A039689 (complement), A296079 (characteristic function).
Cf. also A065512, A078892, A263028, A248792.

[n: n in [1..200] | IsPrime(EulerPhi(n)+1)]; // Vincenzo Librandi, Aug 13 2013

Select[Range[300], PrimeQ[EulerPhi[#] + 1]&] (* Vincenzo Librandi, Aug 13 2013 *)

Edited by N. J. A. Sloane, May 21 2008 at the suggestion of R. J. Mathar

A296079 a(n) = 1 if 1+phi(n) is prime, 0 otherwise, where phi = A000010, Euler totient function.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0

Offset: 1

Antti Karttunen, Dec 05 2017

nonn

Out of the first 65537 values, 26197 are 1's (indicating primes), and 39340 are 0's, indicating nonprimes.

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for characteristic functions

Characteristic function of A039698.
Cf. A039689 (positions of zeros).
Cf. also A296077, A296078, A296080.

Table[If[PrimeQ[EulerPhi[n]+1],1,0],{n,120}] (* Harvey P. Dale, Apr 23 2020 *)

PARI
```
A296079(n) = isprime(1+eulerphi(n));
```

a(n) = A010051(A039649(n)) = A010051(1+A000010(n)).

For all n, a(n) >= A010051(n) and a(2n) >= A010051(n).

A263029 Numbers n such that A002322(n) + 1 is not a prime, where A002322 is Carmichael lambda.

Original entry on oeis.org

25, 32, 50, 55, 75, 81, 96, 100, 110, 115, 119, 121, 128, 150, 153, 160, 162, 165, 176, 187, 200, 203, 209, 215, 220, 221, 224, 230, 235, 238, 242, 245, 253, 256, 261, 275, 287, 288, 289, 295, 297, 299, 300, 306, 319, 323, 324, 330, 335, 343, 345, 355

Offset: 1

Vincenzo Librandi, Oct 12 2015

Complement of A263028.

Antti Karttunen, Table of n, a(n) for n = 1..25794

Cf. A002322, A263027, A263028.
Positions of zeros in A296077.
Cf. also A039689.

[n: n in [2..400] | not IsPrime(CarmichaelLambda(n)+1)];

Select[Range[1, 400], ! PrimeQ[CarmichaelLambda[#] + 1] &]

for(n=1, 1e3, if(isprime((1 + lcm(znstar(n)[2]))) == 0, print1(n", "))) \\ Altug Alkan, Oct 12 2015

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A039698 Numbers k such that phi(k) + 1 is prime.

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A296079 a(n) = 1 if 1+phi(n) is prime, 0 otherwise, where phi = A000010, Euler totient function.

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A263029 Numbers n such that A002322(n) + 1 is not a prime, where A002322 is Carmichael lambda.

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