A263027 -id:A263027 - 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

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

A296076 Least number with the same prime signature as 1 + A002322(n), where A002322 is Carmichael's lambda.

Original entry on oeis.org

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 12, 2, 2, 2, 4, 2

Offset: 1

Antti Karttunen, Dec 05 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A002322, A046523, A263027, A263028 (positions of 2's), A296077, A296078.

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A296076(n) = A046523(1+lcm(znstar(n)[2]));

a(n) = A046523(A263027(n)) = A046523(1+A002322(n)).

cp's OEIS Frontend

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

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A296076 Least number with the same prime signature as 1 + A002322(n), where A002322 is Carmichael's lambda.

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