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Indices k such that A011772(k) is even.
4

%I #19 Jun 15 2022 14:36:08

%S 3,5,7,9,10,11,12,13,17,18,19,21,23,25,26,27,29,31,34,35,36,37,39,41,

%T 42,43,44,47,48,49,50,53,55,56,57,58,59,61,67,68,70,71,73,74,75,76,78,

%U 79,80,81,82,83,84,85,88,89,93,97,98,99,100,101,103,104,105,106,107,108,109,110,111,113,114,117,119

%N Indices k such that A011772(k) is even.

%H N. J. A. Sloane, <a href="/A344000/b344000.txt">Table of n, a(n) for n = 1..9196</a>

%o (Python)

%o from sympy.ntheory.modular import crt

%o from sympy import factorint

%o from math import prod

%o from itertools import count, islice, combinations

%o def A344000_gen(): # generator of terms

%o for n in count(1):

%o plist = tuple(p**q for p, q in factorint(2*n).items())

%o if len(plist) > 1 and min(min(crt((m,2*n//m),(0,-1))[0],crt((2*n//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))) & 1 == 0:

%o yield n

%o A344000_list = list(islice(A344000_gen(),40)) # _Chai Wah Wu_, Jun 15 2022

%Y Cf. A011772, A343999, A344001.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jun 01 2021