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a(n) = A344005(2*n+1).
2

%I #11 Jul 06 2021 20:24:26

%S 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 17,52,10,18,58,60,27,25,66,23,70,72,24,21,78,80,82,34,29,88,13,30,19,

%U 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 a(n) = A344005(2*n+1).

%C The companion bisection to A011772.

%F a(n) = 2*n if 2*n+1 is a prime power. - _Chai Wah Wu_, Jul 06 2021

%o (Python 3.8+)

%o from itertools import combinations

%o from math import prod

%o from sympy import factorint, divisors

%o from sympy.ntheory.modular import crt

%o def A345444(n):

%o if n == 0:

%o return 1

%o k = 2*n+1

%o plist = [p**q for p, q in factorint(k).items()]

%o 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 Cf. A011772, A344005.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jul 06 2021