|
%I #31 Feb 17 2022 00:34:55
%S 39,60,70,95,119,240,2079,2130,2183,3000,3125,3431,4250,6293,6468,
%T 9310,10164,10241,10679,13433,14039,14111,15561,16199,16799,23552,
%U 24601,27004,28116,28560,31416,32883,42112,44268,52193,52969,53754,59072
%N Numbers k such that sopfr(k) = sopfr(k + sopfr(k)).
%C sopfr(k) = sum of the prime factors of k (with multiplicity).
%H Paolo P. Lava, <a href="/A050780/b050780.txt">Table of n, a(n) for n = 1..201</a> [offset shifted by _Georg Fischer_, Oct 17 2019]
%e sopfr(39) = 3 + 13 = 16 = 5 + 11 = sopfr(39 + sopfr(39)), so 39 is in the sequence.
%t sopf[n_] := Total[Apply[Times, FactorInteger[n], {1}]]; ok[n_] := n + sopf[n] - sopf[n + sopf[n]] == n; Select[Range[59200], ok] (* _Jean-François Alcover_, Apr 18 2011 *)
%o (Magma) f:=func<n|&+[j[1]*j[2]: j in Factorization(n)]>; [k:k in [2..60000]| f(k) eq f(k+f(k))]; // _Marius A. Burtea_, Oct 17 2019
%Y Cf. A001414, A050781, A050703, A050704, A050705, A050706, A050707, A050708, A050709, A050710.
%K nonn,nice
%O 1,1
%A _Patrick De Geest_, Sep 15 1999
%E Edited by _Jon E. Schoenfield_, Dec 25 2016
%E Offset changed to 1 by _Jon E. Schoenfield_, Oct 17 2019
|
