OFFSET
1,1
COMMENTS
Numbers such that bigomega(n) - omega(n) = 1 and bigomega(n+1) - omega(n+1) = 1, where bigomega(n) is the number of primes dividing n (counted with repetition) and omega(n) is the number of distinct primes dividing n. - Michel Lagneau, Dec 17 2011
This sequence has 3548 terms up to 10^5, 35340 up to 10^6, 353147 up to 10^7, and 3531738 up to 10^8, suggesting a natural density around 0.0353.... - Charles R Greathouse IV, Mar 06 2017
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Indranil Ghosh)
Indranil Ghosh, Python program to generate the sequence.
MATHEMATICA
Select[Range[1400], PrimeOmega[#]-PrimeNu[#] == 1 && PrimeOmega[#+1] - PrimeNu[#+1] == 1 &] (* Indranil Ghosh, Mar 05 2017 *)
SequencePosition[Table[PrimeOmega[n]-PrimeNu[n], {n, 1500}], {1, 1}][[;; , 1]] (* Harvey P. Dale, Jul 17 2024 *)
PROG
(PARI) isok(n) = (bigomega(n)-omega(n) == 1) && (bigomega(n+1)-omega(n+1) == 1); \\ Michel Marcus, Mar 05 2017
(PARI) is(n)=factorback(factor(n)[, 2])==2 && factorback(factor(n+1)[, 2])==2 \\ Charles R Greathouse IV, Mar 06 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Jason Earls, Jul 11 2003
STATUS
approved