cp's OEIS Frontend

A364496 Numbers k such that k is a multiple of A163511(k).

%I A364496 #21 Sep 02 2023 11:24:53
%S A364496 0,3,6,12,24,48,96,192,384,768,1536,3072,6144,12288,16383,24576,32766,
%T A364496 49152,65532,98304,131064,196608,262128,393216,524256,786432,1048512,
%U A364496 1572864,2097024,3145728,4194048,6291456,8388096,12582912,16776192,25165824,33552384,50331648,67104768,100663296,134209536,201326592
%N A364496 Numbers k such that k is a multiple of A163511(k).
%C A364496 If n is present, then 2*n is also present, and vice versa.
%C A364496 A007283 is included as a subsequence, because it gives the known fixed points of map n -> A163511(n).
%C A364496 Sequence A243071(A364497(.)) sorted into ascending order.
%H A364496 Antti Karttunen, <a href="/A364496/b364496.txt">Table of n, a(n) for n = 1..53</a>
%e A364496 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 A364496 536870895 is present, because A163511(536870895) = 1177 (11*107), which divides 536870895 (3*5*11*47*107*647). See also example in A364498.
%o A364496 (PARI)
%o A364496 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A364496 A054429(n) = ((3<<#binary(n\2))-n-1);
%o A364496 A163511(n) = if(!n,1,A005940(1+A054429(n)))
%o A364496 isA364496(n) = !(n%A163511(n));
%Y A364496 Positions of 1's in A364492.
%Y A364496 Subsequence of A364292.
%Y A364496 Cf. A007283 (subsequence), A163511, A364963 (odd terms).
%Y A364496 Cf. also A364295, A364494, A364497, A364498.
%K A364496 nonn
%O A364496 1,2
%A A364496 _Antti Karttunen_, Jul 27 2023