A296076 -id:A296076 - cp's OEIS frontend

A296078 Least number with the same prime signature as 1+phi(n), where phi = A000010, Euler totient function.

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

Offset: 1

Antti Karttunen, Dec 05 2017

nonn

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

Cf. A000010, A046523, A039649, A296079, A296080.
Cf. A039698 (positions of 2's).
Cf. also A277906, A296076, A296085, A296092.

f[n_] := Block[{ps = Last@# & /@ FactorInteger[1 + EulerPhi@n]}, Times @@ ((Prime@ Range@ Length@ ps)^ps)]; Array[f, 105] (* Robert G. Wilson v, Dec 11 2017 *)

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
A296078(n) = A046523(1+eulerphi(n));

a(n) = A046523(A039649(n)) = A046523(1+A000010(n)).

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

Original entry on oeis.org

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)).

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

A296092 Least number with the same prime signature as sigma(n)+1.

Original entry on oeis.org

2, 4, 2, 8, 2, 2, 4, 16, 6, 2, 2, 2, 6, 4, 4, 32, 2, 24, 6, 2, 6, 2, 4, 2, 32, 2, 2, 6, 2, 2, 6, 64, 4, 6, 4, 12, 6, 2, 6, 6, 2, 2, 12, 6, 2, 2, 4, 8, 6, 6, 2, 12, 6, 4, 2, 4, 16, 6, 2, 4, 12, 2, 30, 128, 6, 6, 6, 2, 2, 6, 2, 36, 12, 6, 8, 6, 2, 4, 16, 6, 6, 2, 6, 36, 2, 6, 4, 2, 6, 6, 2, 4, 6, 6, 4, 6, 12, 12, 2, 6, 2, 6, 30, 2, 2

Offset: 1

Antti Karttunen, Dec 07 2017

nonn

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

Cf. A000203, A046523, A088580, A296212.

Cf. also A276528, A296076, A296078, A296085, A296091.

(define (A296092 n) (A046523 (+ 1 (A000203 n))))

a(n) = A046523(A088580(n)) = A046523(1+A000203(n)).

cp's OEIS Frontend

A296078 Least number with the same prime signature as 1+phi(n), where phi = A000010, Euler totient function.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

A296092 Least number with the same prime signature as sigma(n)+1.

Views

Author

Keywords

Links

Crossrefs

Programs

Scheme

Formula