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 A270415 #12 Apr 13 2025 14:51:15 %S A270415 3,5,10,17,26,65,65537,146690,703922,1481090,1885130,2036330,2211170, %T A270415 2430482,2505890,5470922,9840770,11607650,17783090,24137570,74425130, %U A270415 76615010,77563250,133379402,138697730,138980522,142396490,155575730,177715562,181899170 %N A270415 Numbers n such that sigma(n-1) and sigma(n) - 1 are both primes. %C A270415 Numbers n such that A000203(n-1) and A039653(n) are both primes. %C A270415 Intersection of A270413 and A248792. %C A270415 Prime terms are in A249759. %C A270415 Corresponding values of sigma(n-1): 3, 7, 13, 31, 31, 127, 131071, ... %C A270415 Corresponding values of sigma(n) - 1: 3, 5, 17, 17, 41, 83, 65537, ... %e A270415 17 is in the sequence because sigma(17-1) = sigma(16) = 31 and sigma(10) - 1 = 18 - 1 = 17 (both primes). %t A270415 Select[Range[10^7], And[PrimeQ@ DivisorSigma[1, # - 1], PrimeQ[DivisorSigma[1, #] - 1]] &] (* _Michael De Vlieger_, Mar 17 2016 *) %o A270415 (Magma) [n: n in [2..10000000] | IsPrime(SumOfDivisors(n-1)) and IsPrime(SumOfDivisors(n)-1)]; %o A270415 (PARI) isok(n) = isprime(sigma(n-1)) && isprime(sigma(n)-1); \\ _Michel Marcus_, Mar 17 2016 %Y A270415 Cf. A000203, A039653, A248792, A249759, A270413. %K A270415 nonn %O A270415 1,1 %A A270415 _Jaroslav Krizek_, Mar 16 2016