A102299 Number of prime divisors with multiplicity of n where n and n+1 are composite or twin composite numbers.

3, 2, 2, 2, 3, 2, 4, 2, 2, 3, 5, 2, 2, 2, 2, 2, 3, 3, 5, 2, 3, 2, 4, 2, 4, 2, 2, 3, 6, 2, 3, 2, 2, 3, 3, 2, 5, 4, 4, 2, 2, 2, 4, 2, 3, 2, 2, 2, 3, 3, 4, 3, 3, 2, 3, 2, 3, 3, 2, 2, 5, 2, 2, 2, 3, 3, 7, 2, 4, 2, 2, 4, 4, 2, 2, 2, 6, 2, 2, 3, 4, 3, 3, 2, 2, 2, 6, 2, 3, 3, 5, 2, 3, 3, 3, 3, 5, 2, 3, 2, 4, 2, 3, 2, 3

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Example

For n=8 n+1=9 a twin composite pair. 8=2*2*2 or product of 3 prime divisors with multiplicity.

Mathematica

Total[Transpose[FactorInteger[#]][[2]]]&/@Transpose[Select[Partition[Complement[Range[250], Prime[Range[PrimePi[250]]]], 2, 1], #[[2]]-#[[1]]==1&]][[1]] (* Harvey P. Dale, Nov 25 2010 *)

Prog

(PARI) f1(n) = for(x=1, n, y=composite(x); if(!isprime(y+1), print1(bigomega(y)", "))) composite(n) =\The n-th composite number. 1 is def as not prime nor composite. { local(c, x); c=1; x=1; while(c <= n, x++; if(!isprime(x), c++); ); return(x) }

Crossrefs

Sequence in context: A207384 A085034 A119323 * A302481 A306542 A335171

Adjacent sequences: A102296 A102297 A102298 * A102300 A102301 A102302

Keyword

easy,nonn

Author

Cino Hilliard, Feb 19 2005

Status

approved