A278291 Numbers n such that n-1 has the same number of prime factors as n (with multiplicity).

3, 10, 15, 22, 26, 28, 34, 35, 39, 45, 58, 76, 86, 87, 94, 95, 99, 117, 119, 122, 123, 125, 134, 136, 142, 143, 146, 148, 154, 159, 165, 171, 172, 175, 178, 202, 203, 206, 214, 215, 218, 219, 231, 245, 246, 254, 285, 286, 297, 299, 302, 303, 327, 333, 335, 351, 357, 362, 370, 376, 382, 388, 394, 395

Offset: 1

Author

Ely Golden, Nov 16 2016

Keywords

• nonn

Examples

			a(1)=3, as both 2 and 3 have 1 prime factor. a(2)=10, as both 9 and 10 have 2 prime factors. a(3)=15, as both 14 and 15 have 2 prime factors.
		

Links

• Ely Golden, Table of n, a(n) for n = 1..10000

Programs

Java

public class A278291{
public static void main(String[] args)throws Exception{
    long dim0=numberOfPrimeFactors(2);//note that this method must be manually implemented by the user
    long dim1;
    long counter=3;
    long index=1;
    while(index<=10000){
      dim1=numberOfPrimeFactors(counter);
      if(dim1==dim0){System.out.println(index+" "+counter);index++;}
      dim0=dim1;
      counter++;
    }
  }
}

Mathematica

fQ[n_] := PrimeOmega[n - 1] == PrimeOmega[n]; Select[Range@400, fQ] (* Robert G. Wilson v, Nov 17 2016 *)

PARI

is(n) = bigomega(n)==bigomega(n-1) \\ Felix Fröhlich, Nov 17 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);
counter=3
index=1
while(index<=10000):
    dim1=bigomega(counter);
    if(dim1==dim0):
        print(str(index)+" "+str(counter))
        index+=1;
    dim0=dim1;
    counter+=1;

Formula

a(n) = A045920(n) + 1. - Robert G. Wilson v, Nov 17 2016