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%I #13 Mar 16 2024 17:26:07
%S 1,0,0,0,0,1,0,0,0,3,0,5,0,5,7,0,0,7,0,11,11,9,0,13,0,11,0,17,0,20,0,
%T 0,19,15,23,23,0,17,23,27,0,30,0,29,31,21,0,29,0,23,31,35,0,25,39,41,
%U 35,27,0,48
%N a(n) = n - (sum of prime power components of n).
%C a(n) = 0 iff n is a prime power p^a, a >= 1.
%C Contribution from _Daniel Forgues_, Nov 16 2009: (Start)
%C a(n) = (product of prime power components of n) - (sum of prime power components of n).
%C a(1) = (product of prime power components of 1) - (sum of prime power components of 1)
%C a(1) = (empty product) - (empty sum) = 1 - 0 = 1. (End)
%H Daniel Forgues, <a href="/A086664/b086664.txt">Table of n, a(n) for n = 1..100000</a>
%F a(n) = n - A008475(n).
%e a(1) = 1 - (0) = 1,
%e a(8) = 8 - (2^3) = 0,
%e a(10) = 10 - (2^1 + 5^1) = 3.
%t Join[{1}, Array[# - Total[MapApply[Power, FactorInteger[#]]] &, 100, 2]] (* _Paolo Xausa_, Mar 16 2024 *)
%o (PARI) sof(n)=local(x); x=factor(n); sum(i=1,length(x[,1]),x[i,1]^x[i,2]); for(i=1,60,print1(i-sof(i)","))
%Y Cf. A008475.
%K nonn
%O 1,10
%A _Jon Perry_, Jul 27 2003
%E Corrected (a(1) changed from 0 to 1) and edited by _Daniel Forgues_, Nov 14 2009
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