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%I #9 Sep 23 2016 16:22:34
%S 0,5,12,22,35,35,70,51,51,70,176,70,247,117,92,92,425,92,532,117,145,
%T 247,782,117,145,330,117,176,1247,145,1426,145,287,532,210,145,2035,
%U 651,376,176,2501,210,2752,330,176,925,3290,176,287,210,590,425,4187
%N s(3s-1)/2 where s is the sum of the prime factors of n (with repetition).
%H Harvey P. Dale, <a href="/A074376/b074376.txt">Table of n, a(n) for n = 1..1000</a>
%H Neville Holmes, <a href="http://www.comp.utas.edu.au/users/nholmes/sqncs/cmbntns.htm#A074376">Integer Sequence Combinations</a> [Broken link?]
%e a(20) = 9(3*9-1)/2 = 117 because 9 = 2+2+5 and 20 = 2*2*5.
%t spf[n_]:=Module[{t=Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[ n]]]},(t(3t-1))/2]; Join[{0},Array[spf,60,2]] (* _Harvey P. Dale_, Sep 23 2016 *)
%o (PARI) sopfr(n) = my(f=factor(n)); sum(k=1, matsize(f)[1], f[k, 1]*f[k, 2])
%o fn(n) = my(s=sopfr(n)); s*(3*s-1)/2 \\ _Michel Marcus_, Jul 11 2013
%Y Applies A000326 to A001414. Cf. A074373, A074374, A074375.
%K easy,nonn
%O 1,2
%A _W. Neville Holmes_, Aug 29 2002
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