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 A357906 #15 Oct 05 2023 04:05:26 %S A357906 0,0,1,1,2,1,1,2,1,2,1,2,2,1,3,3,2,1,1,3,2,1,1,3,2,2,1,2,2,3,1,3,2,2, %T A357906 3,2,2,1,3,4,2,2,1,2,3,1,1,4,1,2,3,3,2,1,3,3,2,2,1,4,2,1,2,3,4,2,1,3, %U A357906 2,3,1,3,2,2,3,2,2,3,1,5,1,2,1,3,4,1,3,3,2,3,3,2,2,1,3,4,2,1,2,3 %N A357906 a(n) = log_2(A073103(n)). %H A357906 Jianing Song, <a href="/A357906/b357906.txt">Table of n, a(n) for n = 1..10000</a> %F A357906 Additive with a(2) = 0, a(4) = 1, a(8) = 2, a(2^e) = 3, e >= 4; a(p^e) = 2 for p == 1 (mod 4), 1 for p == 3 (mod 4). %e A357906 a(16) = 3 since x^4 == 1 (mod 16) has 2^3 = 8 solutions. %t A357906 f[p_, e_] := If[Mod[p, 4] == 1, 2, 1]; f[2, e_] := Switch[e, 1, 0, 2, 1, 3, 2, _, 3]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 05 2023 *) %o A357906 (PARI) a(n)=my(f=factor(n)); sum(i=1, #f~, if(f[i, 1]==2, min(f[i, 2]-1, 3), if(f[i, 1]%4==1, 2, 1))) \\ after _Charles R Greathouse IV_'s program for A073103 %Y A357906 Cf. A073103, A072273, A357905. %K A357906 nonn,easy %O A357906 1,5 %A A357906 _Jianing Song_, Oct 19 2022