A364546 - OEIS

%I #9 Jul 28 2023 16:05:42

%S 1,2,3,4,5,6,8,10,12,16,20,24,32,40,48,64,80,96,128,160,192,256,320,

%T 384,512,640,768,1024,1035,1280,1536,2048,2070,2560,3072,4096,4140,

%U 5120,6144,8192,8280,10240,12288,16384,16560,20480,24576,32768,33120,40960,49152,65536,66240,81920,98304,131072,132480,163840

%N Numbers k such that k is a multiple of A005940(k).

%C Sequence A005941(A364548(.)) sorted into ascending order.

%C If k is a term, then also 2*k is present in this sequence, and vice versa.

%C A029747 is included as a subsequence, because it gives the known fixed points of map n -> A005940(n).

%t nn = 2^18; Array[Set[a[#], #] &, 2]; Do[If[EvenQ[n], Set[a[n], 2 a[n/2]], Set[a[n], Times @@ Power @@@ Map[{Prime[PrimePi[#1] + 1], #2} & @@ # &, FactorInteger[a[(n + 1)/2]]]]], {n, 3, nn}]; Select[Range[nn], Divisible[#, a[#]] &] (* _Michael De Vlieger_, Jul 28 2023 *)

%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 isA364546(n) = !(n%A005940(n));

%Y Positions of 1's in A364502.

%Y Subsequence of A364541.

%Y Subsequences: A029747, A364547 (odd terms).

%Y Cf. A005940, A364544, A364548.

%Y Cf. also A364496.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 28 2023