A364544 Numbers k such that k divides A005940(k).

1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 40, 48, 64, 80, 96, 125, 128, 160, 192, 245, 250, 256, 320, 375, 384, 490, 500, 512, 640, 715, 750, 768, 845, 847, 980, 1000, 1024, 1215, 1280, 1430, 1500, 1536, 1690, 1694, 1960, 2000, 2048, 2430, 2560, 2860, 2873, 3000, 3072, 3380, 3388, 3920, 4000, 4096, 4860, 5120

Offset

1,2

Comments

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..63.

Mathematica

nn = 5120; 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 };
isA364544(n) = !(A005940(n)%n);

Crossrefs

Positions of 1's in A364501.

Subsequence of A364542.

Subsequences: A029747, A364545 (odd terms).

Cf. A005940.

Cf. also A364494, A364546.

Sequence in context: A245709 A364565 A364548 * A253789 A364546 A364550

Adjacent sequences: A364541 A364542 A364543 * A364545 A364546 A364547

Keyword

nonn

Author

Antti Karttunen, Jul 28 2023

Status

approved