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A278291 Numbers n such that n-1 has the same number of prime factors as n (with multiplicity). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 31 07:51 EDT 2021. Contains 346369 sequences. (Running on oeis4.)