A296079 -id:A296079 - 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

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

Original entry on oeis.org

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)).

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

A296212 a(n) = 1 if sigma(n) + 1 is prime, 0 otherwise.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Dec 07 2017

nonn

Characteristic function of A065512, numbers n such that sigma(n) + 1 is prime.

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

Cf. A000203, A010051, A065512, A088580, A296092.

Cf. also A296077, A296079, A296211.

(define (A296212 n) (A010051 (+ 1 (A000203 n))))

a(n) = A010051(1+A000203(n)) = A010051(A088580(n)).

cp's OEIS Frontend

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

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

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

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A296212 a(n) = 1 if sigma(n) + 1 is prime, 0 otherwise.

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