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

1, 2, 56, 98, 102, 198, 402, 611, 780, 981, 1230, 1275, 1377, 2288, 3685, 4030, 6600, 8851, 9282, 11371, 11607, 13680, 15390, 15862, 16445, 20916, 21266, 21867, 22606, 27504, 27538, 29282, 30685, 31832, 32724, 34153, 34293, 35672, 38805, 38874, 39886, 43706, 44253, 44772, 45408, 47742, 48032

Offset: 1

Author

Robert Israel, Oct 06 2024

Keywords

• nonn

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Maple

sopfr:= proc(k) option remember; local t;
  add(t[1]*t[2],t=ifactors(k)[2])
end proc:
filter:= proc(k) local s;
 s:= sopfr(k);
 sopfr(k+s) = s + sopfr(s)
end proc:
select(filter, [$1..10^5]);

Mathematica

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