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.

A328246 Numbers whose third arithmetic derivative (A099306) is a squarefree number (A005117).

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%I A328246 #6 Oct 11 2019 16:56:25
%S A328246 9,14,18,21,25,33,38,46,49,57,65,77,85,93,98,121,126,129,134,138,141,
%T A328246 145,150,161,166,177,185,186,194,201,205,206,209,217,221,237,242,249,
%U A328246 253,258,262,265,266,289,290,301,305,306,315,322,326,333,334,338,341,342,350,361,365,369,375,377,381,393,398,402,413,414
%N A328246 Numbers whose third arithmetic derivative (A099306) is a squarefree number (A005117).
%C A328246 Numbers n for which A008966(A003415(A003415(A003415(n)))) = 1.
%H A328246 Antti Karttunen, <a href="/A328246/b328246.txt">Table of n, a(n) for n = 1..10000</a>
%e A328246 For n=9, its first arithmetic derivative is A003415(9) = 6, its second derivative is A003415(6) = 5, and its third derivative is A003415(5) = 1, and 1 is a squarefree number (in A005117), thus 9 is included in this sequence.
%e A328246 For n=14, A003415(14) = 9, A003415(9) = 6, A003415(6) = 5, and 5, like all primes, is a squarefree number, thus 14 is included in this sequence.
%e A328246 For n=49, A003415(49) = 14, A003415(14) = 9, A003415(9) = 6 = 2*3, and 6 is a squarefree number, thus 49 is included in this sequence.
%o A328246 (PARI)
%o A328246 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328246 isA328246(n) = { my(u=A003415(A003415(A003415(n)))); (u>0 && issquarefree(u)); };
%Y A328246 Cf. A003415, A005117, A008966, A099306, A328234, A328244, A328245.
%Y A328246 Cf. A192192, A328239, A328247 (subsequences).
%K A328246 nonn
%O A328246 1,1
%A A328246 _Antti Karttunen_, Oct 11 2019