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Search: id:A133828
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| A133828 |
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a(n) = the smallest "isolated divisor" of n. A positive divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n. |
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+0
2
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| 1, 0, 1, 4, 1, 6, 1, 4, 1, 5, 1, 6, 1, 7, 1, 4, 1, 6, 1, 10, 1, 11, 1, 6, 1, 13, 1, 4, 1, 10, 1, 4, 1, 17, 1, 6, 1, 19, 1, 8, 1, 14, 1, 4, 1, 23, 1, 6, 1, 5, 1, 4, 1, 6, 1, 4, 1, 29, 1, 10, 1, 31, 1, 4, 1, 6, 1, 4, 1, 5, 1, 6, 1, 37, 1, 4, 1, 6, 1, 8, 1, 41, 1, 12, 1, 43, 1, 4, 1, 15, 1, 4, 1, 47, 1, 6, 1
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(2n-1) = 1 for all positive integers n. 2 has no isolated divisors. a(2) is 0 only as a place-holder.
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EXAMPLE
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a(18)=6 because the isolated divisors of 18 are 6,9, and 18.
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MAPLE
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with(numtheory): a:=proc(n) local div, ISO, i: div:=divisors(n): ISO:={}: for i to tau(n) do if member(div[i]-1, div)=false and member(div[i]+1, div) = false then ISO := `union`(ISO, {div[i]}) end if end do end proc: 1, 0, seq(a(j)[1], j=3..80); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 16 2007
A133828 := proc(n) local divs, k, i ; divs := sort(convert(numtheory[divisors](n), list)) ; for i from 1 to nops(divs) do k := op(i, divs) ; if not k-1 in divs and not k+1 in divs then RETURN(k) ; fi ; od: RETURN(0) ; end: seq(A133828(n), n=1..100) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 19 2007
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CROSSREFS
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Cf. A133779, A133829.
Sequence in context: A127168 A109039 A109040 this_sequence A144907 A010779 A136706
Adjacent sequences: A133825 A133826 A133827 this_sequence A133829 A133830 A133831
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Sep 25 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2007
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