cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A364544 #9 Jul 28 2023 15:54:32
%S A364544 1,2,3,4,5,6,8,10,12,16,20,24,32,40,48,64,80,96,125,128,160,192,245,
%T A364544 250,256,320,375,384,490,500,512,640,715,750,768,845,847,980,1000,
%U A364544 1024,1215,1280,1430,1500,1536,1690,1694,1960,2000,2048,2430,2560,2860,2873,3000,3072,3380,3388,3920,4000,4096,4860,5120
%N A364544 Numbers k such that k divides A005940(k).
%C A364544 If k is a term, then also 2*k is present in this sequence, and vice versa.
%C A364544 A029747 is included as a subsequence, because it gives the known fixed points of map n -> A005940(n).
%t A364544 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 *)
%o A364544 (PARI)
%o A364544 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A364544 isA364544(n) = !(A005940(n)%n);
%Y A364544 Positions of 1's in A364501.
%Y A364544 Subsequence of A364542.
%Y A364544 Subsequences: A029747, A364545 (odd terms).
%Y A364544 Cf. A005940.
%Y A364544 Cf. also A364494, A364546.
%K A364544 nonn
%O A364544 1,2
%A A364544 _Antti Karttunen_, Jul 28 2023