A248792 Numbers n such that sigma(n) - 1 is a prime p.

2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 20, 21, 23, 24, 26, 29, 30, 31, 33, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 51, 52, 53, 55, 57, 58, 59, 60, 61, 63, 65, 67, 71, 73, 74, 76, 78, 79, 83, 84, 85, 86, 88, 89, 90, 92, 93, 96, 97, 101, 103, 105, 107, 109

Offset

1,1

Comments

Union of primes (A000040) and terms of A066073 (composites).

Numbers n such that A039653(n) is prime.

Corresponding values of primes p are in A248793.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Example

6 is in sequence because sigma(6) - 1 = 12 - 1 = 11 (prime).

Maple

with(numtheory): A248792:=n->`if`(isprime(sigma(n)-1), n, NULL): seq(A248792(n), n=1..200); # Wesley Ivan Hurt, Jul 09 2015

Mathematica

Select[Range[110], PrimeQ[DivisorSigma[1, #] - 1] &] (* Vincenzo Librandi, Nov 02 2014 *)

Prog

(Magma) [n: n in[1..1000] | IsPrime(SumOfDivisors(n) - 1)]
(PARI) for(n=1, 10^3, if(isprime(sigma(n)-1), print1(n, ", "))) \\ Derek Orr, Nov 01 2014

Crossrefs

Cf. A000203 (sum of divisors), A000040 (primes).

Cf. A039653 (sigma(n)-1), A066073 (subsequence of composites), A248793.

Cf. A065512 (numbers n such that sigma(n) + 1 is prime).

Sequence in context: A360477 A122144 A064052 * A358976 A064594 A325511

Adjacent sequences: A248789 A248790 A248791 * A248793 A248794 A248795

Keyword

nonn,easy

Author

Jaroslav Krizek, Nov 01 2014

Status

approved