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A133950 a(n) = the number of "isolated divisors" of n(n+1)/2. A positive divisor k of n is isolated if neither k-1 nor k+1 divides n. 4
1, 2, 1, 2, 4, 4, 4, 5, 6, 4, 5, 5, 4, 8, 10, 6, 6, 6, 6, 8, 8, 4, 8, 12, 6, 8, 11, 6, 8, 8, 8, 14, 8, 8, 14, 9, 4, 8, 16, 8, 8, 8, 6, 16, 12, 4, 12, 17, 9, 12, 13, 6, 8, 16, 18, 18, 8, 4, 11, 11, 4, 12, 28, 20, 16, 8, 6, 13, 16, 8, 14, 14, 4, 12, 19, 14, 16, 8, 12, 31, 10, 4, 11, 22, 8, 8, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Ray Chandler, Table of n, a(n) for n=1..10000

FORMULA

a(n) = A063440(n) - A133949(n) = A132881(A000217(n)).

EXAMPLE

a(8)=5 because 36 (=8*9/2) has 5 isolated divisors: 6,9,12,18,36.

MAPLE

with(numtheory): b:=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: seq(nops(b((1/2)*j*(j+1))), j=1..80); # Emeric Deutsch, Oct 15 2007

CROSSREFS

Cf. A133948, A133949, A063440.

Sequence in context: A264569 A265601 A105970 * A241512 A094265 A153898

Adjacent sequences:  A133947 A133948 A133949 * A133951 A133952 A133953

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 30 2007

EXTENSIONS

More terms from Emeric Deutsch, Oct 15 2007

Extended by Ray Chandler, Jun 23 2008

STATUS

approved

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Last modified November 17 16:08 EST 2019. Contains 329241 sequences. (Running on oeis4.)