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 A307137 #39 Nov 22 2024 13:57:42
%S A307137 68,17500,5053176,435034872,3079148398,107924794257,122918945808,
%T A307137 63602175290616,27232626132792608,131685306017557752
%N A307137 Terms of A194269 that are not squares of primes.
%C A307137 A194269 lists the integers j that satisfy Sum_{i=1..k} d(i)^i = j+1 for some k where d() is the sorted list of divisors of j.
%C A307137 All squares of primes (A001248) are in A194269 (with k=2), but some terms of A194269 are not in A001248.
%C A307137 So the sequence consists of the integers that satisfy Sum_{i=1..k} d(i)^i = j+1 for k > 2.
%C A307137 a(1) = 68 = 1 + 2^2 + 4^3 is the only term with k = 3; the others should have k > 3. - _Max Alekseyev_, Nov 18 2024
%C A307137 Also in the sequence is 1125089196456707568267636780. - _Daniel Suteu_, Mar 28 2019
%C A307137 146891545244361186001164385301664828062299990188246080274986418 and 1074195891803336036687617104130500495489848428998310547357799403665 are also terms. - _Giovanni Resta_, Mar 29 2019
%C A307137 No other terms below 10^22. Also contains 1397818536728878029228901636216061803887128332853093401018283627886158780 and 187-digit number Sum_{i=1..52} A027750(734441344,i)^i. - _Max Alekseyev_, Nov 22 2024
%e A307137 The divisors of 68 are 1, 2, 4, 17, 34, 68; 1^1 + 2^2 + 4^3 = 69, so 68 is a term.
%o A307137 (PARI) isok1(n) = {my(d=divisors(n), s=0); for(k=1, #d, s += d[k]^k; if (s == n+1, return (k)); if (s > n+1, break););0;} \\ A194269
%o A307137 isok(n) = isok1(n) && isprimepower(n)!=2;
%Y A307137 Cf. A001248, A194269.
%K A307137 nonn,more
%O A307137 1,1
%A A307137 _Michel Marcus_, Mar 26 2019
%E A307137 a(6)-a(7) from _Giovanni Resta_, Mar 29 2019
%E A307137 a(8)-a(10) from _Daniel Suteu_ confirmed by _Max Alekseyev_, Nov 18 2024