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%I #28 Aug 18 2024 04:30:35
%S 2,3,5,7,13,19,29,37,43,61,67,73,101,109,137,149,157,163,173,193,197,
%T 199,211,229,241,257,277,281,283,313,317,331,337,347,349,353,367,373,
%U 379,397,401,409,421,457,461,463,487,499,509,523,541
%N Primes p such that there is a unique solution to p = sigma(x) - 1.
%H Amiram Eldar, <a href="/A066076/b066076.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%F If A066075(m) = 1, then prime(m) is a term.
%t 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 *)
%o (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
%o (PARI) is(n) = isprime(n) && invsigmaNum(n + 1) == 1; \\ _Amiram Eldar_, Aug 18 2024, using _Max Alekseyev_'s invphi.gp
%Y Cf. A000040, A000203, A058340, A066071, A066072, A066073, A066074, A066075, A066076, A066077, A066080.
%K nonn
%O 1,1
%A _Labos Elemer_, Dec 03 2001