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 A349988 #32 Dec 31 2023 12:36:17
%S A349988 3,5,2,1,11,10,3,10,19,3,10,1,1,29,26,3,5,3,3,2,2,1,10,1,3,10,5,2,9,3,
%T A349988 1,5,10,3,39,10,1,7,21,1,5,5,3,21,7,2,5,10,1,78,10,3,2,26,3,10,5,1,7,
%U A349988 1,3,1,10,3,21,7,1,3,68,3,2,5,1,21,26,1,5,2,3
%N A349988 a(n) is the smallest k such that n^k + (n+1)^k is divisible by a square > 1.
%C A349988 a(285) <= 111. - _Kevin P. Thompson_, Jan 13 2022
%H A349988 Kevin P. Thompson, <a href="/A349988/b349988.txt">Table of n, a(n) for n = 1..284</a>
%H A349988 Kevin P. Thompson, <a href="/A349988/a349988.txt">Factorizations to support a(n) for n = 1..284</a>
%F A349988 a(9m-5) = 1 for m >= 1 since a(9m-5) = (9m-5)^1 + (9m-5+1)^1 = 18m-9 which is divisible by 9 = 3^2. - _Kevin P. Thompson_, Jan 13 2022
%F A349988 a(n) = 1 if n is in A046092; in this case, if n = A046092(m), then n^1 + (n+1)^1 = (2*m+1)^2. - _Bernard Schott_, Jan 17 2022
%e A349988 a(2) = 5 since the values of 2^k + (2+1)^k for k=1..4 are 5, 13, 35, and 97, none of which are divisible by a square > 1, and 2^5 + (2+1)^5 = 275 which is divisible by 25 = 5^2.
%t A349988 Table[k=1;While[SquareFreeQ[n^k+(n+1)^k],k++];k,{n,33}] (* _Giorgos Kalogeropoulos_, Dec 08 2021 *)
%o A349988 (PARI) a(n) = my(k=1); while(issquarefree(n^k + (n+1)^k), k++); k; \\ _Michel Marcus_, Dec 08 2021
%Y A349988 Cf. A046092, A280302, A280547, A289629, A289985, A349989.
%K A349988 nonn
%O A349988 1,1
%A A349988 _Jon E. Schoenfield_, Dec 07 2021
%E A349988 Thanks to _Hugo Pfoertner_ for computing terms a(50) and a(68).