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 A385326 #17 Jul 02 2025 19:09:35 %S A385326 1,3,2,2,3,2,2,7,4,2,7,2,2,3,2,6,6,5,2,6,4,6,7,2,2,12,2,5,6,2,2,21,10, %T A385326 2,6,2,8,7,5,2,3,2,21,6,8,15,18,5,4,6,2,2,17,2,6,6,8,5,19,9,2,12,2,18, %U A385326 18,2,14,7,4,2,6,4,10,7,2,10,12,15,6,6,4,2,16,2,2,19,2,5,6,2,2,6,10,9,21,2,4,32,2,2,6 %N A385326 The number of positive k <= 2*n + 1 such that 2*n + 1 divides (2^k + 2*n + 1)^2 - 1. %e A385326 1 is the term because 2*0 + 1 = 1 is divisor of (2^1 + 2*0 + 1)^2 - 1 = 3^2 - 1 = 8. %t A385326 a[n_]:=Length[Select[Range[2n+1],Divisible[(2^#+2n+1)^2-1,2n+1] &]]; Array[a,101,0] (* _Stefano Spezia_, Jun 25 2025 *) %o A385326 (Magma) [#[k: k in [1..2*n+1] | ((2^k+2*n+1)^2 - 1) mod (2*n + 1) eq 0]: n in [0..100]]; %o A385326 (PARI) a(n) = sum(k=1, 2*n+1, !Mod((2^k + 2*n + 1)^2 - 1, 2*n + 1)); \\ _Michel Marcus_, Jun 25 2025 %Y A385326 Cf. A003462 (numbers m > 0 such that a(m) = 3), A005384 (primes p such that a(p) = 2), A005408 (odd numbers), A076481 (primes q such that a(q) = 3), A081858 (numbers k numbers k >= 0 such that 2k + 1 divides 2^k - 1), A102781 (numbers k such that 2k + 1 divides (2^k + 2*k + 1)^2 - 1), A224486 (numbers k such that 2k + 1 divides 2^k + 1). %K A385326 nonn %O A385326 0,2 %A A385326 _Juri-Stepan Gerasimov_, Jun 25 2025