This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A357841 #10 Nov 19 2022 21:50:41 %S A357841 4,27,85,121,166,265,517,526,634,706,778,913,985,1633,1822,1966,2173, %T A357841 2218,2326,2434,2605,2785,3505,3802,3865,3973,4306,4369,4765,4918, %U A357841 5248,5674,5818,5926,6178,6385,7186,7726,8185,8257,8653,9193,9301,10201,10489,10606 %N A357841 Smith numbers (A006753) for which the arithmetic derivative (A003415) is also a Smith number. %e A357841 4 = A006753(1) and 4' = 4, so 4 is a term. %e A357841 27 = A006753(3) and 27' = 27, so 27 is a term. %e A357841 85 = A006753(5) and 85' = 22 = A006753(2), so 85 is a term. %t A357841 digsum[n_] := Total@IntegerDigits[n]; smithQ[n_] := CompositeQ[n] && Plus @@ (Last[#]*digsum[First@#] & /@ FactorInteger[n]) == digsum[n]; d[0] = d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[10^4], smithQ[#] && smithQ[d[#]] &] (* _Amiram Eldar_, Oct 21 2022 *) %o A357841 (Magma) sm:=func<n| not IsPrime(n) and (&+Intseq(n) eq &+[ Factorisation(n)[i][2]* &+Intseq(Factorisation(n)[i][1]) : i in [1..#PrimeDivisors(n)]])>; f:=func<h |h le 1 select 0 else h*(&+[Factorisation(h)[i][2] / Factorisation(h)[i][1]: i in [1..#Factorisation(h)]])>; [n:n in [2..10700]|sm(n) and sm(Floor(f(n)))]; %Y A357841 Cf. A003415, A006753. %K A357841 nonn,base %O A357841 1,1 %A A357841 _Marius A. Burtea_, Oct 20 2022