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%I #26 Mar 31 2022 21:59:53
%S 1,4,6,8,10,11,14,14,15,17,22,19,26,23,23,24,34,26,38,29,31,35,46,33,
%T 35,41,36,39,58,40,62,42,47,53,47,46,74,59,55,51,82,54,86,59,56,71,94,
%U 59,63,62,71,69,106,65,71,69,79,89,118,72,122,95,76,76,83,82,134,89,95,84,142
%N a(n) = n + (sum of prime factors of n taken with repetition).
%C a(n) = n + A001414(n).
%H Reinhard Zumkeller, <a href="/A075254/b075254.txt">Table of n, a(n) for n = 1..10000</a>
%e a(6)=11 because 6=2*3, sopfr(6)=2+3=5 and 6+5=11.
%p A075254 := proc(n)
%p n+A001414(n) ;
%p end proc: # _R. J. Mathar_, Jul 27 2015
%t Table[If[n==1,1, n +Plus@@Times@@@FactorInteger@n], {n, 80}] (* _G. C. Greubel_, Jan 10 2019 *)
%o (Haskell)
%o a075254 n = n + a001414 n -- _Reinhard Zumkeller_, Feb 27 2012
%o (PARI) a(n) = my(f = factor(n)); n += sum(k=1, #f~, f[k,1]*f[k,2]); \\ _Michel Marcus_, Feb 22 2017
%o (Magma) [n eq 1 select 1 else (&+[p[1]*p[2]: p in Factorization(n)]) + n: n in [1..80]]; // _G. C. Greubel_, Jan 10 2019
%o (Sage) [n + sum(factor(n)[j][0]*factor(n)[j][1] for j in range(0, len(factor(n)))) for n in range(1, 80)] # _G. C. Greubel_, Jan 10 2019
%Y Cf. A001414, A008472, A075255.
%Y Cf. A096461 (iteration).
%K nonn
%O 1,2
%A _Zak Seidov_, Sep 10 2002
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