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A376851 Numbers k such that sopfr(k + sopfr(k)) = sopfr(k) + sopfr(sopfr(k)), where sopfr = A001414.

%I A376851 #13 Oct 09 2024 09:12:18
%S A376851 1,2,56,98,102,198,402,611,780,981,1230,1275,1377,2288,3685,4030,6600,
%T A376851 8851,9282,11371,11607,13680,15390,15862,16445,20916,21266,21867,
%U A376851 22606,27504,27538,29282,30685,31832,32724,34153,34293,35672,38805,38874,39886,43706,44253,44772,45408,47742,48032
%N A376851 Numbers k such that sopfr(k + sopfr(k)) = sopfr(k) + sopfr(sopfr(k)), where sopfr = A001414.
%H A376851 Robert Israel, <a href="/A376851/b376851.txt">Table of n, a(n) for n = 1..1000</a>
%e A376851 a(4) = 98 is a term because sopfr(98) = 2 + 2*7 = 16, sopfr(16) = 4 * 2 = 8, and sopfr(98 + 16) = sopfr(114) = 2 + 3 + 19 = 24 = 16 + 8.
%p A376851 sopfr:= proc(k) option remember; local t;
%p A376851   add(t[1]*t[2],t=ifactors(k)[2])
%p A376851 end proc:
%p A376851 filter:= proc(k) local s;
%p A376851  s:= sopfr(k);
%p A376851  sopfr(k+s) = s + sopfr(s)
%p A376851 end proc:
%p A376851 select(filter, [$1..10^5]);
%t A376851 f[n_] := Plus @@ Times @@@ FactorInteger@ n; Select[Range[48400], f[#+f[#]]==f[#]+f[f[#]]&] (* _James C. McMahon_, Oct 09 2024 *)
%Y A376851 Cf. A001414, A376830, A376831, A376843, A376844, A376848, A376849.
%K A376851 nonn
%O A376851 1,2
%A A376851 _Robert Israel_, Oct 06 2024