A258276 Balanced sphenic numbers (of order one): sphenic numbers (A007304) that are the average of the previous sphenic number and the following sphenic number.

186, 370, 406, 418, 518, 582, 602, 710, 786, 814, 826, 830, 942, 978, 994, 1010, 1034, 1070, 1162, 1310, 1374, 1394, 1570, 1630, 1686, 1758, 1886, 1978, 2014, 2114, 2158, 2270, 2274, 2278, 2294, 2438, 2510, 2534, 2570, 2630, 2666, 2690, 2774, 2778, 2782, 2806

Offset: 1

Author

Antonio Roldán, May 25 2015

Keywords

• nonn

Examples

			406 is in this sequence because 406 = A007304(45) = (402+410)/2 = (A007304(44) + A007304(46))/2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006562, A007304, A213025, A245289.

Programs

Mathematica

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 *)

PARI

issphenic(n)=if(n>0,omega(n)==3&&bigomega(n)==3,0)
nextsph(n)={local(k=n+1);while(!issphenic(k),k+=1);k}
precsph(n)={local(k=n-1);while(!issphenic(k)&&k>0,k-=1);k}
{for(i=1,4*10^3,if(issphenic(i)&&2*i== nextsph(i)+ precsph(i),print1(i, ", ")))}