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A278294 a(n) = first term in A278291 with n prime factors.

%I A278294 #45 Dec 05 2016 11:48:28
%S A278294 3,10,28,136,945,5265,29889,50625,203392,3290625,6082048,32536000,
%T A278294 326481921,3274208001,6929459200,72523096065,37694578689,471672487936,
%U A278294 11557226700801,54386217385984,50624737509376,275892612890625,4870020829413376,68091093855502336,2280241934368768
%N A278294 a(n) = first term in A278291 with n prime factors.
%C A278294 a(n)-1 is the first term in A115186 with n prime factors, by definition.
%C A278294 If f(n) is the index of the first occurrence of n in A278293, a(n)=A278291(f(n)), by definition.
%H A278294 Ely Golden, <a href="/A278294/b278294.txt">Table of n, a(n) for n = 1..25</a>
%e A278294 a(2)=10, as it is the first term of A278291 with 2 prime factors.
%e A278294 a(3)=28, as it is the first term of A278291 with 3 prime factors.
%t A278294 Function[w, Flatten@ Map[w[[#]] &, #] &@ Map[First, DeleteCases[#, w_ /; Length@ w == 0]] &@ Map[Position[w, k_ /; PrimeOmega@k == #] &, Range@ 9]]@ Select[Range[10^6], Equal @@ Map[PrimeOmega, {# - 1, #}] &] (* _Michael De Vlieger_, Dec 01 2016 *)
%o A278294 (Java) import java.math.BigInteger;
%o A278294 public class A278294{
%o A278294 public static void main(String[] args)throws Exception{
%o A278294     BigInteger dim0=numberOfPrimeFactors(BigInteger.valueOf(2));//note that this method must be manually implemented by the user
%o A278294     BigInteger dim1;
%o A278294     BigInteger maxdim=BigInteger.ONE;
%o A278294     BigInteger counter=BigInteger.valueOf(3);
%o A278294     long index=1;
%o A278294     while(index<=20){
%o A278294       dim1=numberOfPrimeFactors(counter);
%o A278294       if(dim1.equals(dim0)&&maxdim.testBit(dim1.intValue())==false){System.out.println(dim1+" "+counter);maxdim=maxdim.setBit(dim1.intValue());index++;}
%o A278294       dim0=dim1;
%o A278294       counter=counter.add(BigInteger.ONE);
%o A278294     }
%o A278294   }
%o A278294 }
%o A278294 (SageMath)
%o A278294 def bigomega(x):
%o A278294     s=0;
%o A278294     f=list(factor(x));
%o A278294     for c in range(len(f)):
%o A278294         s+=f[c][1]
%o A278294     return s;
%o A278294 dim0=bigomega(2);
%o A278294 maxdim=1
%o A278294 counter=3
%o A278294 index=1
%o A278294 while(index<=20):
%o A278294     dim1=bigomega(counter);
%o A278294     if((dim1==dim0)&((maxdim&(1<<dim1))==0)):
%o A278294         print(str(index)+" "+str(counter))
%o A278294         maxdim=maxdim|(1<<dim1);
%o A278294         index+=1;
%o A278294     dim0=dim1;
%o A278294     counter+=1;
%Y A278294 Cf. A115186.
%K A278294 nonn
%O A278294 1,1
%A A278294 _Ely Golden_, Nov 16 2016