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 A278294 a(n) = first term in A278291 with n prime factors. 1
 3, 10, 28, 136, 945, 5265, 29889, 50625, 203392, 3290625, 6082048, 32536000, 326481921, 3274208001, 6929459200, 72523096065, 37694578689, 471672487936, 11557226700801, 54386217385984, 50624737509376, 275892612890625, 4870020829413376, 68091093855502336, 2280241934368768 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n)-1 is the first term in A115186 with n prime factors, by definition. If f(n) is the index of the first occurrence of n in A278293, a(n)=A278291(f(n)), by definition. LINKS Ely Golden, Table of n, a(n) for n = 1..25 EXAMPLE a(2)=10, as it is the first term of A278291 with 2 prime factors. a(3)=28, as it is the first term of A278291 with 3 prime factors. MATHEMATICA 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 *) PROG (Java) import java.math.BigInteger; public class A278294{ public static void main(String[] args)throws Exception{     BigInteger dim0=numberOfPrimeFactors(BigInteger.valueOf(2)); //note that this method must be manually implemented by the user     BigInteger dim1;     BigInteger maxdim=BigInteger.ONE;     BigInteger counter=BigInteger.valueOf(3);     long index=1;     while(index<=20){       dim1=numberOfPrimeFactors(counter);       if(dim1.equals(dim0)&&maxdim.testBit(dim1.intValue())==false){System.out.println(dim1+" "+counter); maxdim=maxdim.setBit(dim1.intValue()); index++; }       dim0=dim1;       counter=counter.add(BigInteger.ONE);     }   } } (SageMath) def bigomega(x):     s=0;     f=list(factor(x));     for c in range(len(f)):         s+=f[c][1]     return s; dim0=bigomega(2); maxdim=1 counter=3 index=1 while(index<=20):     dim1=bigomega(counter);     if((dim1==dim0)&((maxdim&(1<

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Last modified August 5 06:46 EDT 2020. Contains 336209 sequences. (Running on oeis4.)