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Numbers k such that k divides A163511(k).
9

%I #7 Jul 27 2023 08:17:38

%S 1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,105,128,144,192,210,256,

%T 288,384,420,429,512,576,768,840,858,1024,1152,1365,1536,1617,1680,

%U 1716,2048,2304,2730,3072,3234,3360,3432,3887,4096,4235,4608,5460,6144,6468,6720,6864,7774,8192,8470,9216,10829,10920,12288

%N Numbers k such that k divides A163511(k).

%C If n is present, then 2*n is also present, and vice versa.

%C A007283 is included as a subsequence, because it gives the known fixed points of map n -> A163511(n).

%o (PARI)

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

%o A054429(n) = ((3<<#binary(n\2))-n-1);

%o A163511(n) = if(!n,1,A005940(1+A054429(n)))

%o isA364494(n) = !(A163511(n)%n);

%Y Positions of 1's in A364491.

%Y Cf. A163511.

%Y Subsequences: A007283, A029744, A364495 (odd terms).

%Y Cf. also A364295, A364496, A364497.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 27 2023