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Numbers k such that k is a multiple of A163511(k).
9

%I #21 Sep 02 2023 11:24:53

%S 0,3,6,12,24,48,96,192,384,768,1536,3072,6144,12288,16383,24576,32766,

%T 49152,65532,98304,131064,196608,262128,393216,524256,786432,1048512,

%U 1572864,2097024,3145728,4194048,6291456,8388096,12582912,16776192,25165824,33552384,50331648,67104768,100663296,134209536,201326592

%N Numbers k such that k is a multiple of 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).

%C Sequence A243071(A364497(.)) sorted into ascending order.

%H Antti Karttunen, <a href="/A364496/b364496.txt">Table of n, a(n) for n = 1..53</a>

%e 16383 is present, because A163511(16383) = 43, as 16383 = 2^14 - 1 and A000040(14) = 43, and 43 is a factor of 16383 = 3*43*127.

%e 536870895 is present, because A163511(536870895) = 1177 (11*107), which divides 536870895 (3*5*11*47*107*647). See also example in A364498.

%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 isA364496(n) = !(n%A163511(n));

%Y Positions of 1's in A364492.

%Y Subsequence of A364292.

%Y Cf. A007283 (subsequence), A163511, A364963 (odd terms).

%Y Cf. also A364295, A364494, A364497, A364498.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 27 2023