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A245636
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Number of terms of A245630 <= n.
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3
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1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
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OFFSET
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1,6
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LINKS
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FORMULA
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As n -> infinity, a(n)/sqrt(n) -> Product_{i=1..infinity} (1 - 1/prime(i))/(1 - (prime(i)*prime(i+1))^(-1/2)), see Erdős reference.
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EXAMPLE
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The first two terms of A245630 are 1 and 6, so a(n) = 1 for 1 <= n <= 5 and a(6) = 2.
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MAPLE
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N:= 10^4: # to get a(1) to a(N)
PP:= [seq(ithprime(i)*ithprime(i+1), i=1.. numtheory[pi](floor(sqrt(N)))-1)]:
ext:= (x, p) -> seq(x*p^i, i=0..floor(log[p](N/x))):
S:= {1}: for i from 1 to nops(PP) do S:= map(ext, S, PP[i]) od:
E:= Array(1..N):
for s in S do E[s]:= 1 od:
A:= map(round, Statistics:-CumulativeSum(E)):
seq(A(i), i=1..N);
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MATHEMATICA
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M = 10^4;
T = Table[Prime[n] Prime[n+1], {n, 1, PrimePi[Sqrt[M]]}];
T2 = Select[Join[T, T^2], # <= M&];
S = Join[{1}, T2 //. {a___, b_, c___, d_, e___} /; b*d <= M && FreeQ[{a, b, c, d, e}, b*d] :> Sort[{a, b, c, d, e, b*d}]];
ee = Table[0, {M}];
Scan[Set[ee[[#]], 1]&, S];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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