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

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

Offset: 1

Author

Ely Golden, Nov 16 2016

Keywords

• nonn

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.

Examples

			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.
		

Links

• Ely Golden, Table of n, a(n) for n = 1..25

Crossrefs

Cf. A115186.

Programs

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);
    }
  }
}

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 *)

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<