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Numbers k such that sopfr(k + sopfr(k)) = sopfr(k) + sopfr(sopfr(k)), where sopfr = A001414.
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%I #13 Oct 09 2024 09:12:18

%S 1,2,56,98,102,198,402,611,780,981,1230,1275,1377,2288,3685,4030,6600,

%T 8851,9282,11371,11607,13680,15390,15862,16445,20916,21266,21867,

%U 22606,27504,27538,29282,30685,31832,32724,34153,34293,35672,38805,38874,39886,43706,44253,44772,45408,47742,48032

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

%H Robert Israel, <a href="/A376851/b376851.txt">Table of n, a(n) for n = 1..1000</a>

%e 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 sopfr:= proc(k) option remember; local t;

%p add(t[1]*t[2],t=ifactors(k)[2])

%p end proc:

%p filter:= proc(k) local s;

%p s:= sopfr(k);

%p sopfr(k+s) = s + sopfr(s)

%p end proc:

%p select(filter, [$1..10^5]);

%t f[n_] := Plus @@ Times @@@ FactorInteger@ n; Select[Range[48400], f[#+f[#]]==f[#]+f[f[#]]&] (* _James C. McMahon_, Oct 09 2024 *)

%Y Cf. A001414, A376830, A376831, A376843, A376844, A376848, A376849.

%K nonn

%O 1,2

%A _Robert Israel_, Oct 06 2024