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.

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

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: A265601 A349816 A105970 * A241512 A360095 A350659

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