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Difference between n-th prime power and its arithmetic derivative.
6

%I #10 Apr 16 2014 02:33:11

%S 1,1,2,0,4,6,-4,3,10,12,-16,16,18,22,15,0,28,30,-48,36,40,42,46,35,52,

%T 58,60,-128,66,70,72,78,-27,82,88,96,100,102,106,108,112,99,50,126,

%U -320,130,136,138,148,150,156,162,166,143,172,178,180,190,192,196

%N Difference between n-th prime power and its arithmetic derivative.

%C a(n) = A000961(n)-A192015(n) = A000961(n)-A003415(A000961(n)) = A192133(n)*A025473(n)^(A025474(n)-1) = A192133(n)*A000961(n)/A025473(n);

%C a(A095874(A000040(n))) = A006093(n);

%C a(A095874(A001248(n))) = A005722(n) + 1.

%H Reinhard Zumkeller, <a href="/A192134/b192134.txt">Table of n, a(n) for n = 1..10000</a>

%o (Haskell)

%o a192134 n = a000961 n - a192015 n -- _Reinhard Zumkeller_, Apr 16 2014

%K sign

%O 1,3

%A _Reinhard Zumkeller_, Jun 26 2011