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 A345444 #11 Jul 06 2021 20:24:26 %S A345444 1,2,4,6,8,10,12,5,16,18,6,22,24,26,28,30,11,14,36,12,40,42,9,46,48, %T A345444 17,52,10,18,58,60,27,25,66,23,70,72,24,21,78,80,82,34,29,88,13,30,19, %U A345444 96,44,100,102,14,106,108,36,112,45,26,34,120,41,124,126,42,130,56,54,136,138,47,65,29 %N A345444 a(n) = A344005(2*n+1). %C A345444 The companion bisection to A011772. %F A345444 a(n) = 2*n if 2*n+1 is a prime power. - _Chai Wah Wu_, Jul 06 2021 %o A345444 (Python 3.8+) %o A345444 from itertools import combinations %o A345444 from math import prod %o A345444 from sympy import factorint, divisors %o A345444 from sympy.ntheory.modular import crt %o A345444 def A345444(n): %o A345444 if n == 0: %o A345444 return 1 %o A345444 k = 2*n+1 %o A345444 plist = [p**q for p, q in factorint(k).items()] %o A345444 return k-1 if len(plist) == 1 else int(min(min(crt([m,k//m],[0,-1])[0],crt([k//m,m],[0,-1])[0]) for m in (prod(d) for l in range(1,len(plist)//2+1) for d in combinations(plist,l)))) # _Chai Wah Wu_, Jul 06 2021 %Y A345444 Cf. A011772, A344005. %K A345444 nonn %O A345444 0,2 %A A345444 _N. J. A. Sloane_, Jul 06 2021