A364546 Numbers k such that k is a multiple of A005940(k).

1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 40, 48, 64, 80, 96, 128, 160, 192, 256, 320, 384, 512, 640, 768, 1024, 1035, 1280, 1536, 2048, 2070, 2560, 3072, 4096, 4140, 5120, 6144, 8192, 8280, 10240, 12288, 16384, 16560, 20480, 24576, 32768, 33120, 40960, 49152, 65536, 66240, 81920, 98304, 131072, 132480, 163840

Offset: 1

Author

Antti Karttunen, Jul 28 2023

Keywords

• nonn

Comments

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

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

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

Crossrefs

Positions of 1's in A364502.

Subsequence of A364541.

Subsequences: A029747, A364547 (odd terms).

Cf. A005940, A364544, A364548.

Cf. also A364496.

Programs

Mathematica

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 *)

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
isA364546(n) = !(n%A005940(n));