This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A249760 #27 Apr 22 2025 10:49:19 %S A249760 2,4,16,65536 %N A249760 Numbers k such that k+1 and sigma(k) are both primes. %C A249760 4 is the only number k such that k-1 and sigma(k) are both primes. %C A249760 Corresponding values of k+1 and sigma(k) are in A249759 and A249761. %C A249760 Conjectures: (1) sequence is finite; (2) a(n) + 1 is a Fermat prime (A019434); (3) sigma(a(n)) is a Mersenne prime (A000668). %C A249760 Subsequence of A023194, and by a comment in that entry it follows that each term is a prime power. From that conjectures (2) and (3) above easily follow. - _Jeppe Stig Nielsen_, Jan 13 2015 %F A249760 a(n) = A249759(n) - 1. %e A249760 16 is a term because 16+1=17 and sigma(16)=31 are both primes. %t A249760 Select[Range[10^5], PrimeQ[# + 1]&& PrimeQ[DivisorSigma[1, #]] &] (* _Vincenzo Librandi_, Nov 14 2014 *) %o A249760 (Magma) [n: n in [1..10^8] | IsPrime(n+1) and IsPrime(SumOfDivisors(n))]; %Y A249760 Cf. A000203, A000668, A019434, A249759, A249761. %K A249760 nonn,more %O A249760 1,1 %A A249760 _Jaroslav Krizek_, Nov 13 2014