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%I #13 Jul 08 2015 17:04:43
%S 186,370,406,418,518,582,602,710,786,814,826,830,942,978,994,1010,
%T 1034,1070,1162,1310,1374,1394,1570,1630,1686,1758,1886,1978,2014,
%U 2114,2158,2270,2274,2278,2294,2438,2510,2534,2570,2630,2666,2690,2774,2778,2782,2806
%N Balanced sphenic numbers (of order one): sphenic numbers (A007304) that are the average of the previous sphenic number and the following sphenic number.
%H Giovanni Resta, <a href="/A258276/b258276.txt">Table of n, a(n) for n = 1..10000</a>
%e 406 is in this sequence because 406 = A007304(45) = (402+410)/2 = (A007304(44) + A007304(46))/2.
%t a=30; b=42; c=66; L={}; While[ Length[L]<100, If[b-a == c-b, AppendTo[L, b]]; a=b; b=c++; While[ Last/@ FactorInteger[c] != {1,1,1}, c++]]; L (* _Giovanni Resta_, Jun 09 2015 *)
%o (PARI)
%o issphenic(n)=if(n>0,omega(n)==3&&bigomega(n)==3,0)
%o nextsph(n)={local(k=n+1);while(!issphenic(k),k+=1);k}
%o precsph(n)={local(k=n-1);while(!issphenic(k)&&k>0,k-=1);k}
%o {for(i=1,4*10^3,if(issphenic(i)&&2*i== nextsph(i)+ precsph(i),print1(i, ", ")))}
%Y Cf. A006562, A007304, A213025, A245289.
%K nonn
%O 1,1
%A _Antonio Roldán_, May 25 2015
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