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A137721
Number of numbers not greater than n with no prime gaps in their factorization.
5
1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 17, 17, 17, 18, 19, 20, 20, 21, 21, 22, 23, 24, 25, 25, 25, 26, 27, 28, 28, 28, 28, 29, 29, 30, 30, 31, 31, 32, 33, 34, 34, 34, 34, 35, 36, 36, 36, 36, 36, 37, 38, 39, 39, 39, 40, 40, 40, 41, 41, 41, 41, 42, 43, 44
OFFSET
1,2
COMMENTS
a(n) > a(n-1) iff A073490(n) = 0;
a(n) > A137722(n) for n < 134;
a(n) < A137722(n) for n > 140;
a(A137723(n) + n) = a(A137723(n)) + 1.
Partial sums of A137794. - Reinhard Zumkeller, Feb 11 2008
LINKS
FORMULA
a(n) = Sum_{k=1..n} 0^A073490(k).
MATHEMATICA
b[n_] := With[{pp = PrimePi @ FactorInteger[ n ][[All, 1]]},
Boole[pp[[-1]] - pp[[1]] + 1 == Length[pp]]]; (* b is A137794 *)
Array[b, 105] // Accumulate (* Jean-François Alcover, Dec 09 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 09 2008
STATUS
approved