A066076 Primes p such that there is a unique solution to p = sigma(x) - 1.

2, 3, 5, 7, 13, 19, 29, 37, 43, 61, 67, 73, 101, 109, 137, 149, 157, 163, 173, 193, 197, 199, 211, 229, 241, 257, 277, 281, 283, 313, 317, 331, 337, 347, 349, 353, 367, 373, 379, 397, 401, 409, 421, 457, 461, 463, 487, 499, 509, 523, 541

Offset: 1

Author

Labos Elemer, Dec 03 2001

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

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

Programs

Mathematica

With[{s = KeySort@ PositionIndex@ Array[DivisorSigma[1, #] - 1 &, 10^5]}, Take[#, 51] &@ Keys@ KeySelect[s, PrimeQ@ # && Length@ Lookup[s, #] == 1 &]] (* Michael De Vlieger, Jul 16 2017 *)

PARI

{ n=0; for (m=1, 10^9, p=prime(m); a=1; for (x=1, p - 1, if (p == (sigma(x) - 1), a++; break)); if (a==1, write("b066076.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Nov 10 2009

PARI

is(n) = isprime(n) && invsigmaNum(n + 1) == 1; \\ Amiram Eldar, Aug 18 2024, using Max Alekseyev's invphi.gp

Formula

If A066075(m) = 1, then prime(m) is a term.