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.

A260624 a(n) = arithmetic derivative of the n-th composite number.

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%I A260624 #41 Oct 31 2015 15:52:36
%S A260624 4,5,12,6,7,16,9,8,32,21,24,10,13,44,10,15,27,32,31,80,14,19,12,60,21,
%T A260624 16,68,41,48,39,25,112,14,45,20,56,81,16,92,22,31,92,33,51,192,18,61,
%U A260624 72,26,59,156,39,55,80,18,71,176,108,43,124,22,45,32,140,123
%N A260624 a(n) = arithmetic derivative of the n-th composite number.
%H A260624 Matthew Campbell, <a href="/A260624/b260624.txt">Table of n, a(n) for n = 1..10000</a>; used code by _Altug Alkan_.
%F A260624 a(n) = A003415(A002808(n)).
%e A260624 The second composite number is 6. 6 = 2 * 3. 6' = 2*3' + 3*2' = 3 * 1 + 2 * 1 = 3 + 2 = 5, so a(2) = 5.
%t A260624 lim = 120; f[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]]; f /@ Rest@ Complement[Range@ lim, Prime@ Range@ PrimePi@ lim] (* _Michael De Vlieger_, Oct 07 2015, after _Michael Somos_ at A003415 *)
%o A260624 (PARI) forcomposite(n=1, 100, if((a(n) = local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))), print1(a(n)", "))); \\ _Altug Alkan_, Oct 06 2015
%Y A260624 Cf. A002808 (composite), A003415 (n').
%Y A260624 Cf. A001787 ((2^n)'), A068719 ((2*n)'), A068720 ((n^2)'), A068721 ((n^3)').
%K A260624 nonn,easy
%O A260624 1,1
%A A260624 _Matthew Campbell_, Oct 06 2015
%E A260624 More terms from _Altug Alkan_, Oct 06 2015