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 A270414 #15 Apr 13 2025 14:52:20 %S A270414 3,5,10,17,65537 %N A270414 Numbers m such that sigma(m-1) and sigma(phi(m)) are both primes. %C A270414 Numbers n such that A000203(n-1) and A062402(n) are both primes. %C A270414 There are no other terms <= 10^7. %C A270414 Intersection of A270413 and A062514. %C A270414 Prime terms are in A249759. %C A270414 Corresponding values of sigma(n-1): 3, 7, 13, 31, 131071, ... %C A270414 Corresponding values of sigma(phi(n)): 3, 7, 7, 31, 131071, ... %C A270414 Conjecture: union of number 10 and A249759. %e A270414 10 is in the sequence because sigma(10-1) = sigma(9) = 13 and sigma(phi(10)) = sigma(4) = 7 (both primes). %t A270414 Select[Range[10^6], And[PrimeQ@ DivisorSigma[1, # - 1], PrimeQ@ DivisorSigma[1, EulerPhi@ #]] &] (* _Michael De Vlieger_, Mar 17 2016 *) %o A270414 (Magma) [n: n in [2..100000] | IsPrime(SumOfDivisors(n-1)) and IsPrime(SumOfDivisors(EulerPhi(n)))]; %o A270414 (PARI) isok(n) = isprime(sigma(n-1)) && isprime(sigma(eulerphi(n))); \\ _Michel Marcus_, Mar 17 2016 %Y A270414 Cf. A000010, A000203, A062514, A249759, A256438, A270413. %K A270414 nonn,more %O A270414 1,1 %A A270414 _Jaroslav Krizek_, Mar 16 2016