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A135063
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Define the sequence {b_n(m)} by b_n(0)=0; b_n(m) = the number of positive divisors of (b_n(m-1)+n), for all m >= 1. Then a(n) is the smallest positive integer such that b_n(m) = b_n(m+a(n)) for all m > some positive integer.
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2
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1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 2, 2, 1, 2, 1, 2, 4, 1, 3, 1, 3, 1, 2, 2, 1, 4, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 2, 3, 1, 2, 2, 5, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 4, 3, 1, 1, 1, 1, 2, 1, 1, 3, 1, 3, 1, 1, 2, 5, 1, 1, 2, 2, 1, 3, 1, 1, 3, 2, 1
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OFFSET
| 1,2
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EXAMPLE
| {b_7(m)} is 0,2,3,4,2,3,4,..., with (2,3,4) repeating thereafter. So a(7) = 3, the length of the repeating subsequence (2,3,4).
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MAPLE
| Contribution from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 09 2010: (Start)
b := proc(n, m) option remember; if m =0 then 0; else numtheory[tau]( procname(n, m-1)+n); end if; end proc:
A135063 := proc(n) bseq := [] ; for m from 0 do bs := b(n, m) ; if member(bs, bseq, 'w') then return 1+nops(bseq)-w ; else bseq := [op(bseq), bs] ; end if; end do: end proc: seq(A135063(n), n=1..120) ; (End)
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CROSSREFS
| Cf. A135062.
Sequence in context: A129265 A030358 A118914 * A124010 A196228 A133364
Adjacent sequences: A135060 A135061 A135062 * A135064 A135065 A135066
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, Nov 15 2007
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EXTENSIONS
| Terms beyond a(12) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 09 2010
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