A067830 Primes p such that sigma(p-4) < p.

5, 7, 11, 17, 23, 41, 47, 71, 83, 101, 107, 113, 131, 167, 197, 227, 233, 281, 311, 317, 353, 383, 401, 443, 461, 467, 491, 503, 617, 647, 677, 743, 761, 773, 827, 857, 863, 881, 887, 911, 941, 971, 1013, 1091, 1097, 1217, 1283, 1301, 1307, 1427, 1433, 1451

Offset: 1

Author

Benoit Cloitre, Feb 08 2002

Keywords

• nonn
• easy

Comments

Except for the first term, terms are primes of the form p+4 with p prime, i.e., the sequence is essentially A031505, A046132. In other words, the solutions to sigma(x) < x + 4 are 1,2,4 and the odd primes. - Ralf Stephan, Feb 09 2004

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A025584, A046022, A067833.

Programs

Mathematica

Select[Prime[Range[3, 230]], DivisorSigma[1, #-4] < # &] (* Amiram Eldar, Apr 25 2025 *)

PARI

isok(p) = isprime(p) && (p>4) && (sigma(p-4) < p); \\ Michel Marcus, Feb 15 2021

Extensions

Edited by Charles R Greathouse IV, Mar 19 2010