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

Author

Jaroslav Krizek, Nov 01 2014

Keywords

• nonn
• easy

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.

Examples

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

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).

Programs

Magma

[n: n in[1..1000] | IsPrime(SumOfDivisors(n) - 1)];

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 *)

PARI

for(n=1,10^3,if(isprime(sigma(n)-1),print1(n,", "))) \\ Derek Orr, Nov 01 2014