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 A063103 #34 Jan 25 2025 03:09:30
%S A063103 3,8,2667,3937,57337,172011,253921,677207307,1073602561,
%T A063103 732959441001382539,750688035198863979,1000923107604038521,
%U A063103 1108158528150703969,196751176038481899983340171,223076247804911695439842851,262302377656070899470360793,262336402488441531425882329
%N A063103 Numbers k such that sigma(usigma(k)) is prime.
%C A063103 a(2) = 8 is the only even term. Each of the odd terms is a product of distinct Mersenne primes (A046528), that have Mersenne exponents (A000043) p_1, p_2, ..., p_m (m >= 1) such that p_1 + p_2 + ... + p_m + 1 is also a Mersenne exponent. - _Amiram Eldar_, Jan 25 2025
%H A063103 Amiram Eldar, <a href="/A063103/b063103.txt">Table of n, a(n) for n = 1..97</a> (terms below 10^1000)
%e A063103 k = 8: usigma(8) = 9 and sigma(9) = 13, a prime.
%e A063103 k = 2667: usigma(2667) = 4096 and sigma(4096) = 8191, a prime.
%t A063103 us[n_Integer] := (d = Divisors[n]; l = Length[d]; k = 1; s = n; While[k < l, If[ GCD[ d[[k]], n/d[[k]] ] == 1, s = s + d[[k]]]; k++ ]; s); Do[m = n; If[ PrimeQ[ DivisorSigma[1, us[n]]], Print[n]], {n, 1, 10^7} ]
%o A063103 (PARI) u(n) = sumdiv(n,d, if(gcd(d, n/d)==1,d)); for(n=1,10^7, if(isprime(sigma(u(n))),print(n)))
%o A063103 (Magma) us:=func<n|&+[d:d in Divisors(n)| Gcd(d,n div d) eq 1]>; [k:k in [1..10^6]| IsPrime(DivisorSigma(1,us(k)))]; // _Marius A. Burtea_, Feb 13 2020
%Y A063103 Cf. A000203, A034448, A063845.
%Y A063103 Cf. A000043, A000668, A046528.
%K A063103 nonn
%O A063103 1,1
%A A063103 _Jason Earls_, Aug 07 2001
%E A063103 a(8)-a(9) from _Donovan Johnson_, Jul 16 2012
%E A063103 a(10)-a(13) from _Manuel Valdivia_, Sep 28 2012
%E A063103 a(14)-a(17) from _Amiram Eldar_, Jan 25 2025