A066073 Composite numbers k such that sigma(k) - 1 is prime.

6, 10, 14, 15, 20, 21, 24, 26, 30, 33, 34, 35, 38, 40, 44, 46, 51, 52, 55, 57, 58, 60, 63, 65, 74, 76, 78, 84, 85, 86, 88, 90, 92, 93, 96, 105, 111, 114, 117, 118, 120, 123, 124, 126, 130, 135, 136, 141, 143, 145, 147, 153, 155, 158, 161, 164, 166, 168, 172, 174

Offset: 1

Author

Labos Elemer, Dec 03 2001

Keywords

• nonn
• easy

Comments

Composite numbers k such that sigma(k) = sigma(p) has a solution in the primes p. - Jaroslav Krizek, Feb 03 2012

Complement of A000040 (primes) with respect to A248792 (numbers n such that sigma(n) - 1 is prime). - Jaroslav Krizek, Nov 13 2014

Numbers k such that sigma(k) - 1 is greater than k and prime. - Giuseppe Coppoletta, Dec 22 2014

Examples

			30, 46, 51, and 55 are in the sequence because each is a composite number n such that sigma(n)-1 = 71, which is prime; 71 itself is excluded from the sequence by definition.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

Cf. A000040, A000203, A058340, A066071, A066072, A066073, A066074, A066075, A066076, A066077, A066080, A248792.

Programs

Maple

filter:= proc(n)
local s;
s:= numtheory:-sigma(n)-1;
  s > n and isprime(s);
end proc:
select(filter, [$2..1000]); # Robert Israel, Dec 22 2014

Mathematica

Do[s=-1+DivisorSigma[1, m]; If[PrimeQ[s]&&!PrimeQ[m], Print[m]], {m, 1, 256}]
Select[Range[200],CompositeQ[#]&&PrimeQ[DivisorSigma[1,#]-1]&] (* Harvey P. Dale, Jan 13 2025 *)

PARI

isA066073(n)=!isprime(n)&&isprime(sigma(n)-1) \\ Charles R Greathouse IV, Feb 20 2012

Sage

[n for n in (2..174) if (sigma(n)-1).is_prime() and sigma(n)-1>n] # Giuseppe Coppoletta, Dec 22 2014