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A178139
Distance between n and the next number with the same number of prime factors (counted with multiplicity).
1
1, 2, 2, 2, 3, 4, 4, 1, 4, 2, 6, 4, 1, 6, 8, 2, 2, 4, 7, 1, 3, 6, 12, 1, 7, 1, 2, 2, 12, 6, 16, 1, 1, 3, 4, 4, 1, 7, 14, 2, 2, 4, 1, 5, 3, 6, 24, 2, 2, 4, 11, 6, 2, 2, 4, 1, 4, 2, 21, 6, 3, 3, 32, 4, 2, 4, 2, 5, 5, 2, 8, 6, 3, 1, 2, 5, 14, 4, 28
OFFSET
2,2
FORMULA
{min d >0: A001222(n+d)= A001222(n)} [R. J. Mathar, May 31 2010]
EXAMPLE
2 is prime. The next prime is 3, and 3-2= 1 = a(2).
For n=3, the next prime is 5, 5-3 = 2 = a(3).
For n=4, the next number with 2 prime factors is 6, 6-4 =2 = a(4).
MATHEMATICA
a1=Array[Plus @@ Last /@ FactorInteger[ # ] &, 400]; a2=Flatten[Position[a1, k]; In a2 putting 1, 2, 3, ...for k gives table of positions of numbers with k factors, repetitions included.
CROSSREFS
Cf. A176884.
Sequence in context: A275444 A243322 A071454 * A039642 A027300 A085313
KEYWORD
nonn
AUTHOR
Daniel Tisdale, May 20 2010
EXTENSIONS
Offset set to 2, and more terms added by R. J. Mathar, May 31 2010
STATUS
approved