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

1,1

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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++;
    }
  }
}
(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;
(PARI) is(n) = bigomega(n)==bigomega(n-1) \\ Felix Fröhlich, Nov 17 2016

Crossrefs

Sequence in context: A112355 A074314 A077759 * A247420 A063231 A224852

Adjacent sequences: A278288 A278289 A278290 * A278292 A278293 A278294

Keyword

nonn

Author

Ely Golden, Nov 16 2016

Status

approved