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A216651
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Lengths of decreasing blocks of A006530, the greatest prime factor of n, starting from the second term.
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2
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1, 2, 2, 2, 1, 1, 2, 4, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 3, 4, 2, 3, 1, 2, 2, 2, 2, 2, 1, 1, 2, 4, 2, 2, 2, 2, 3, 2, 1, 3, 1, 2, 1, 3, 2, 1, 1, 1, 3, 2, 2, 2, 3, 1, 2, 2, 2, 2, 1, 2, 3, 1, 4, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 3, 1, 2, 1, 2, 4, 2, 4, 2, 3, 1, 2, 1
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OFFSET
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1,2
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COMMENTS
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Let gpf(m) be the greatest prime factor of m and the subset E(n) = {m, m+1, ..., m+L-1} such that gpf(m) > gpf(m+1) > ... > gpf(m+L-1) where L is the maximum length of E(n) and n the index such that {E(1) union E(2) union .... } = {2, 3, 4, ...}.
The growth of a(n) is very slow. See the following smallest values of m such that a(m) = n:
a(1) = 1, a(2) = 2, a(20) = 3, a(8) = 4, a(251) = 5, a(936) = 6, a(15553) = 7, a(6380) = 8, a(54838)=9, a(293548) = 10.
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LINKS
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FORMULA
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EXAMPLE
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A006530 with decreasing blocks marked: (2), (3, 2), (5, 3), (7, 2), (3), (5), (11, 3), (13, 7, 5, 2), .... Thus the terms of this sequence are 1, 2, 2, 2, 1, 1, 2, 4, ....
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MAPLE
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L:= map(max @ numtheory:-factorset, [$1..N]):
DL:= L[2..-1]-L[1..-2]:
R:= select(t -> DL[t]>= 0, [$1..N-1]):
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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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