A137371 - OEIS

%I #10 Oct 11 2017 18:13:18

%S 4,6,9,14,22,57,111,218,445,879,1754,3518,7034,14069,28129,56271,

%T 112529,225073,450139,900274,1800559,3601109,7202221,14404439,

%U 28808881,57617759,115235531,230471069,460942121

%N a(n) = least semiprime such that all subsets of {a(1),...,a(n)} have a different sum.

%H S. J. Benkoski and P. Erdős, <a href="http://dx.doi.org/10.1090/S0025-5718-1974-0347726-9">On weird and pseudoperfect numbers</a>, Math. Comp., 28 (1974), pp. 617-623. <a href="http://www.renyi.hu/~p_erdos/1974-24.pdf">Alternate link</a>; <a href="http://dx.doi.org/10.1090/S0025-5718-1975-0360452-6">1975 corrigendum</a>

%p isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true; else false; fi ; end: setsum := proc(S) add(i,i=S) ; end: a := [4] : while true do for anxt from op(-1,a)+1 do if isA001358(anxt) then aset := combinat[powerset](convert(a,set) union {anxt} ); sset := {} ; for s in aset do sset := sset union { setsum(s) } ; od: if nops(sset) = nops(aset) then a := [op(a),anxt] ; print(a) ; break ; fi ; fi ; od: od: # _R. J. Mathar_

%Y Cf. A001358, A006037, A064934.

%K more,nonn

%O 1,1

%A _Jonathan Vos Post_, Apr 09 2008

%E More terms from _R. J. Mathar_

%E a(12)-a(29) from _Donovan Johnson_, Nov 11 2008