A158913 Primes p such that there is a composite c with sigma(p) = sigma(c).

11, 17, 23, 31, 41, 47, 53, 59, 71, 79, 83, 89, 97, 103, 107, 113, 127, 131, 139, 151, 167, 179, 181, 191, 223, 227, 233, 239, 251, 263, 269, 271, 293, 307, 311, 359, 383, 389, 419, 431, 433, 439, 443, 449, 467, 479, 491, 503, 521, 557, 569, 571, 587, 593, 599

Offset: 1

Author

T. D. Noe, Mar 30 2009

Keywords

• nonn

Comments

See A158914 for the sequence for sigma_2.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000203, A158914.

Programs

Mathematica

tp=DivisorSigma[1,Select[Range[1000],PrimeQ]]; tc=DivisorSigma[1,Select[Range[1000],!PrimeQ[ # ]&]]; Intersection[tp,tc]-1

PARI

is(p) = isprime(p) && invsigmaNum(p+1) > 1; \\ Amiram Eldar, Dec 16 2024, using Max Alekseyev's invphi.gp

Sage

[sigma(n)-1 for n in (2..600) if is_prime(sigma(n)-1) and nGiuseppe Coppoletta, Dec 22 2014