Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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