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A083269
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a(n)=Pi[A052180(n)]=A000720[A052180(n)]; Subscript of last prime used in Erathostenes sieve by which all composites between n-th and (n+1)th were omitted.
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2
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0, 1, 1, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 4, 3, 1, 3, 2, 1, 4, 2, 3, 4, 2, 1, 2, 1, 2, 5, 2, 4, 1, 5, 1, 3, 4, 2, 6, 3, 1, 5, 1, 2, 1, 5, 6, 2, 1, 2, 3, 1, 6, 5, 4, 3, 1, 3, 2, 1, 7, 6, 2, 1, 2, 7, 3, 5, 1, 2, 3, 8, 4, 6, 2, 3, 7, 2, 6, 4, 1, 4, 1, 8, 2, 3, 5, 2, 1, 2, 5, 6, 2, 7, 2, 3, 5, 1, 9, 3, 8, 6, 3, 1, 3
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OFFSET
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1,4
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LINKS
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Table of n, a(n) for n=1..105.
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EXAMPLE
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Of composites between 24th and 25th primes (89,97),
the least prime divisors are : {2,7,2,3,2,5,2}.
The largest of these is 7. This means that Pi[7]=4 steps
in prime-sieving is required to sweep out all
composites between 89 and 97: {90,92,94,96},(93},{95} and
{91} were deleted in first,2nd,3rd,4th steps respectively.
So a(24)=4
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MATHEMATICA
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ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] mi[x_] := Min[ba[x]] Table[PrimePi[Max[Table[mi[ba[w]], {w, Prime[j]+1, -1+Prime[j+1]}]]], {j, 1, 30}]
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CROSSREFS
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Cf. A052180, A000720.
Sequence in context: A194066 A182628 A028334 * A097306 A102632 A094076
Adjacent sequences: A083266 A083267 A083268 * A083270 A083271 A083272
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 14 2003
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STATUS
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approved
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