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A343997 a(n) = A011772(n) if that number is even, otherwise A011772(n)+1.

%I A343997 #10 Jun 01 2021 15:36:52
%S A343997 2,4,2,8,4,4,6,16,8,4,10,8,12,8,6,32,16,8,18,16,6,12,22,16,24,12,26,8,
%T A343997 28,16,30,64,12,16,14,8,36,20,12,16,40,20,42,32,10,24,46,32,48,24,18,
%U A343997 40,52,28,10,48,18,28,58,16,60,32,28,128,26,12,66,16,24,20,70,64,72,36,24,56,22,12,78,64,80
%N A343997 a(n) = A011772(n) if that number is even, otherwise A011772(n)+1.
%H A343997 N. J. A. Sloane, <a href="/A343997/b343997.txt">Table of n, a(n) for n = 1..16383</a>
%o A343997 (Python)
%o A343997 from sympy.ntheory.modular import crt
%o A343997 from sympy import factorint
%o A343997 from itertools import product
%o A343997 def A343997(n):
%o A343997     fs = factorint(2*n)
%o A343997     plist = [p**fs[p] for p in fs]
%o A343997     x = min(k for k in (crt(plist,d)[0] for d in product([0,-1],repeat=len(plist))) if k > 0)
%o A343997     return x + x % 2 # _Chai Wah Wu_, Jun 01 2021
%Y A343997 Cf. A000217, A011772, A061781, A343996.
%K A343997 nonn
%O A343997 1,1
%A A343997 _N. J. A. Sloane_, Jun 01 2021