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

1,2

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).

Links

Table of n, a(n) for n=1..58.

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 *)

Prog

(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));

Crossrefs

Positions of 1's in A364502.

Subsequence of A364541.

Subsequences: A029747, A364547 (odd terms).

Cf. A005940, A364544, A364548.

Cf. also A364496.

Sequence in context: A364548 A364544 A253789 * A364550 A029747 A095381

Adjacent sequences: A364543 A364544 A364545 * A364547 A364548 A364549

Keyword

nonn

Author

Antti Karttunen, Jul 28 2023

Status

approved