A248793 Sigma(n) - 1 for n such that sigma(n) - 1 is prime.

2, 3, 5, 11, 7, 17, 11, 13, 23, 23, 17, 19, 41, 31, 23, 59, 41, 29, 71, 31, 47, 53, 47, 37, 59, 89, 41, 43, 83, 71, 47, 71, 97, 53, 71, 79, 89, 59, 167, 61, 103, 83, 67, 71, 73, 113, 139, 167, 79, 83, 223, 107, 131, 179, 89, 233, 167, 127, 251, 97, 101, 103

Offset: 1

Author

Jaroslav Krizek, Nov 01 2014

Keywords

• nonn
• easy

Comments

a(n) = corresponding values of primes p = sigma(A248792(n)) - 1, where A248792(n) = numbers n such that sigma(n) - 1 is prime.

If there are at least two numbers k, h such that a(k) = a(h) = p, then p is in A158913.

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, A000040, A066073, A248792.

Programs

Magma

[a: n in [1..1000] | IsPrime(a) where a is SumOfDivisors(n)-1]

Maple

F:= proc(n)
local r;
r:= numtheory:-sigma(n)-1;
if isprime(r) then r else NULL fi
end proc:
seq(F(n),n=1..1000); # Robert Israel, Nov 02 2014

Mathematica

a248793[n_Integer] :=
Cases[DivisorSigma[1, #] - 1 & /@ Range[n], ?PrimeQ]; a248793[104] (* _Michael De Vlieger, Nov 07 2014 *)

PARI

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

Formula

a(n) = A000203(A248792(n)) - 1.

If A248792(n) is a prime p, then a(n) = A248792(n) = p.