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 A063836 #11 Jan 25 2025 03:09:54
%S A063836 3,217,57337
%N A063836 Numbers k such that usigma(sigma(k)) is prime.
%C A063836 Also, numbers k such that sigma(k) + 1 is a Fermat prime (A019434). Equivalently, numbers k that are a product of distinct Mersenne primes (A000668), k = (2^p_1 - 1) * (2^p_2 - 1) * ... * (2^p_m - 1), p_i are in A000043 and m >= 1, such that p_1 + p_2 + ... + p_m = 2^s and 2^(2^s) + 1 is prime. - _Amiram Eldar_, Jan 25 2025
%t A063836 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[ us[ DivisorSigma[1, n]]], Print[n]], {n, 1, 10^7/4} ]
%o A063836 (PARI) usigma(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]);}
%o A063836 isok(k) = isprime(usigma(sigma(k))); \\ _Amiram Eldar_, Jan 25 2025
%Y A063836 Cf. A000043, A000203, A000668, A019434, A034448, A061765, A063103.
%Y A063836 Subsequence of A046528.
%K A063836 nonn,hard,bref
%O A063836 1,1
%A A063836 _Robert G. Wilson v_, Aug 21 2001