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

1,1

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<<dim1))==0)):
        print(str(index)+" "+str(counter))
        maxdim=maxdim|(1<<dim1);
        index+=1;
    dim0=dim1;
    counter+=1;

Crossrefs

Cf. A115186.

Sequence in context: A239885 A262251 A246974 * A260811 A108912 A350821

Adjacent sequences: A278291 A278292 A278293 * A278295 A278296 A278297

Keyword

nonn

Author

Ely Golden, Nov 16 2016

Status

approved