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Primes p such that there is a composite c with sigma(p) = sigma(c).
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%I #20 Dec 16 2024 01:59:11

%S 11,17,23,31,41,47,53,59,71,79,83,89,97,103,107,113,127,131,139,151,

%T 167,179,181,191,223,227,233,239,251,263,269,271,293,307,311,359,383,

%U 389,419,431,433,439,443,449,467,479,491,503,521,557,569,571,587,593,599

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

%C See A158914 for the sequence for sigma_2.

%H Donovan Johnson, <a href="/A158913/b158913.txt">Table of n, a(n) for n = 1..10000</a>

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).

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

%o (Sage) [sigma(n)-1 for n in (2..600) if is_prime(sigma(n)-1) and n<sigma(n)-1<600] # _Giuseppe Coppoletta_, Dec 22 2014

%o (PARI) is(p) = isprime(p) && invsigmaNum(p+1) > 1; \\ _Amiram Eldar_, Dec 16 2024, using _Max Alekseyev_'s invphi.gp

%Y Cf. A000203, A158914.

%K nonn

%O 1,1

%A _T. D. Noe_, Mar 30 2009