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

39, 60, 70, 95, 119, 240, 2079, 2130, 2183, 3000, 3125, 3431, 4250, 6293, 6468, 9310, 10164, 10241, 10679, 13433, 14039, 14111, 15561, 16199, 16799, 23552, 24601, 27004, 28116, 28560, 31416, 32883, 42112, 44268, 52193, 52969, 53754, 59072

Offset

1,1

Comments

sopfr(k) = sum of the prime factors of k (with multiplicity).

Links

Paolo P. Lava, Table of n, a(n) for n = 1..201 [offset shifted by Georg Fischer, Oct 17 2019]

Example

sopfr(39) = 3 + 13 = 16 = 5 + 11 = sopfr(39 + sopfr(39)), so 39 is in the sequence.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A001414, A050781, A050703, A050704, A050705, A050706, A050707, A050708, A050709, A050710.

Sequence in context: A253436 A253429 A338794 * A039353 A043176 A043956

Adjacent sequences: A050777 A050778 A050779 * A050781 A050782 A050783

Keyword

nonn,nice

Author

Patrick De Geest, Sep 15 1999

Extensions

Edited by Jon E. Schoenfield, Dec 25 2016

Offset changed to 1 by Jon E. Schoenfield, Oct 17 2019

Status

approved