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.

A328239 Numbers whose third arithmetic derivative (A099306) is prime.

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%I A328239 #10 Oct 25 2019 16:57:49
%S A328239 14,18,38,46,138,150,166,186,258,266,322,338,342,350,398,402,502,526,
%T A328239 530,546,550,610,626,658,662,686,717,722,725,726,734,750,758,774,826,
%U A328239 890,931,966,970,1002,1034,1074,1110,1126,1166,1175,1178,1190,1258,1262,1294,1302,1338,1366
%N A328239 Numbers whose third arithmetic derivative (A099306) is prime.
%C A328239 No multiples of 4 because subsequence of A048103.
%H A328239 Antti Karttunen, <a href="/A328239/b328239.txt">Table of n, a(n) for n = 1..10001</a>
%e A328239 A003415(A003415(A003415(14))) = 5, which is a prime, thus 14 is included in this sequence.
%t A328239 dn[0] = 0; dn[1] = 0; dn[n_?Negative] := -dn[-n]; dn[n_] := dn[n] = Module[{f = Transpose[ FactorInteger@n]}, If[ PrimeQ@n, 1, Total[n*f[[2]]/f[[1]]]]]; Select[Range@1390, PrimeQ@ dn@ dn@ dn@# &] (* _Robert G. Wilson v_, Oct 22 2019 *)
%o A328239 (PARI)
%o A328239 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328239 isA328239(n) = isprime(A003415(A003415(A003415(n))));
%Y A328239 Cf. A003415, A099306, A157037, A192192.
%Y A328239 Subsequence of A048103 and of A099308.
%K A328239 nonn
%O A328239 1,1
%A A328239 _Antti Karttunen_, Oct 10 2019