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A050780 Numbers k such that sopfr(k) = sopfr(k + sopfr(k)). 4

%I

%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-Fran├žois 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

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Last modified November 21 01:33 EST 2019. Contains 329349 sequences. (Running on oeis4.)