A263029 -id:A263029 - cp's OEIS frontend

A296077 a(n) = 1 if 1 + A002322(n) is prime, 0 otherwise, where A002322 is Carmichael lambda.

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

Offset: 1

Antti Karttunen, Dec 05 2017

nonn

Out of the first 65537 values, 39743 are 1's (indicating primes), and 25794 are 0's, indicating nonprimes.

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

Characteristic function for A263028.

Cf. A002322, A010051, A263027, A263029 (positions of zeros), A296076, A296079.

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

A296077(n) = isprime(1+lcm(znstar(n)[2]));

a(n) = A010051(A263027(n)) = A010051(1+A002322(n)).

A263028 Numbers n such that A002322(n) + 1 is a prime, where A002322 is Carmichael lambda.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83

Offset: 1

Vincenzo Librandi, Oct 12 2015

Complement of A263029.

Antti Karttunen, Table of n, a(n) for n = 1..39743

Cf. A002322, A263027, A263029, A296077 (characteristic function).

Cf. also A039698.

[1] cat [n: n in [2..100] | IsPrime(CarmichaelLambda(n)+1)];

Select[Range[1, 100], PrimeQ[CarmichaelLambda[#] + 1] &]

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

More terms from Antti Karttunen, Dec 05 2017

A263027 a(n) = A002322(n) + 1, where A002322 is Carmichael lambda.

Original entry on oeis.org

2, 2, 3, 3, 5, 3, 7, 3, 7, 5, 11, 3, 13, 7, 5, 5, 17, 7, 19, 5, 7, 11, 23, 3, 21, 13, 19, 7, 29, 5, 31, 9, 11, 17, 13, 7, 37, 19, 13, 5, 41, 7, 43, 11, 13, 23, 47, 5, 43, 21, 17, 13, 53, 19, 21, 7, 19, 29, 59, 5, 61, 31, 7, 17, 13, 11, 67, 17, 23, 13, 71, 7

Offset: 1

Vincenzo Librandi, Oct 08 2015

nonn

The function t(k,n) = A002322(n)+k provides many prime values for k=1: for n up to 1000, for example, it returns 798 primes (with repetitions). On the other hand, for n <= 1000 and odd k from 3 to 11, t(k,n) gives 247, 387, 538, 231, 504 prime values, respectively.

Another function of this type is |A002322(n)-119|, which provides 693 prime values for n <= 1000. [Bruno Berselli, Oct 14 2015]

Antti Karttunen, Table of n, a(n) for n = 1..5000

Cf. A002322.
Cf. A263028: indices n for which a(n) is prime.
Cf. A263029: indices n for which a(n) is composite.
Cf. also A039649, A296076, A296077.

[2] cat [CarmichaelLambda(n)+1: n in [2..100]];

Table[CarmichaelLambda[n] + 1, {n, 1, 100}]

vector(100, n, 1 + lcm(znstar(n)[2])) \\ Altug Alkan, Oct 08 2015

Edited by Bruno Berselli, Oct 14 2015

A039689 Numbers k such that phi(k) + 1 is not a prime.

Original entry on oeis.org

15, 16, 20, 24, 25, 30, 33, 35, 39, 44, 45, 50, 51, 52, 56, 64, 65, 66, 68, 69, 70, 72, 78, 80, 81, 84, 85, 87, 90, 92, 96, 102, 104, 105, 112, 116, 120, 121, 123, 128, 129, 130, 136, 138, 140, 141, 143, 144, 147, 155, 156, 159, 160, 161, 162, 164, 165, 168, 170

Offset: 1

Olivier Gérard

			phi(20)+1 = 8+1 = 9 is not prime.

Antti Karttunen, Table of n, a(n) for n = 1..39340

Cf. A000010, A007614, A039649, A039698 (complement).
Positions of zeros in A296079.
Cf. also A263029.

Select[Range[200],!PrimeQ[EulerPhi[#]+1]&] (* Harvey P. Dale, Aug 31 2018 *)

isok(k) = !isprime(eulerphi(k)+1); \\ Michel Marcus, Jun 28 2021

Name edited by Antti Karttunen, Dec 05 2017

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A296077 a(n) = 1 if 1 + A002322(n) is prime, 0 otherwise, where A002322 is Carmichael lambda.

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A263028 Numbers n such that A002322(n) + 1 is a prime, where A002322 is Carmichael lambda.

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A263027 a(n) = A002322(n) + 1, where A002322 is Carmichael lambda.

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A039689 Numbers k such that phi(k) + 1 is not a prime.

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