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%I #12 May 06 2015 18:32:58
%S -2,0,3,8,15,13,35,20,18,29,99,25,143,53,34,32,255,28,323,41,58,125,
%T 483,33,50,173,27,65,783,40,899,36,130,293,74,28,1295,365,178,41,1599,
%U 60,1763,137,31,533,2115,25,98,44,298,185,2703,13,146,57,370,845
%N a(n) = sopfr(n)^2 - 2n, where sopfr(n) is the sum of the prime factors of n with multiplicity.
%C If n is prime, then a(n) = n*(n-2). If n is semiprime, then a(n) gives the sum of the squares of the prime factors of n (with multiplicity).
%C a(n) is negative for n = 1, 81, 90, 96, 100, 108, 120, 125, 126, 128, 135, .... - _Charles R Greathouse IV_, May 06 2015
%F a(n) = A074373(n) - A005843(n).
%e a(6) = sopfr(6)^2 - 2(6) = (2+3)^2 - 12 = 25 - 12 = 13.
%e a(8) = sopfr(8)^2 - 2(8) = (2+2+2)^2 - 16 = 36 - 16 = 20.
%t sopfr[n_] := Plus @@ Times @@@ FactorInteger@n; f[1] = 0; Table[sopfr[n]^2 - 2 n, {n, 100}]
%o (PARI) sopfr(n)=my(f=factor(n)); sum(i=1,#f~, f[i,1]*f[i,2])
%o a(n)=sopfr(n)^2 - 2*n \\ _Charles R Greathouse IV_, May 06 2015
%Y Cf. A074373 (sopfr^2), A001414 (sopfr).
%K sign
%O 1,1
%A _Wesley Ivan Hurt_, May 05 2015
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