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A133828 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. 2
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; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(2n-1) = 1 for all positive integers n. 2 has no isolated divisors. a(2) is 0 only as a placeholder.

LINKS

Table of n, a(n) for n=1..97.

EXAMPLE

a(18)=6 because the isolated divisors of 18 are 6,9 and 18.

MAPLE

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, 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, Oct 19 2007

CROSSREFS

Cf. A133779, A133829.

Sequence in context: A109039 A257656 A109040 * A144907 A185093 A010779

Adjacent sequences:  A133825 A133826 A133827 * A133829 A133830 A133831

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 25 2007

EXTENSIONS

More terms from Emeric Deutsch and R. J. Mathar, Oct 16 2007

STATUS

approved

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Last modified March 5 11:57 EST 2021. Contains 341823 sequences. (Running on oeis4.)