

A132895


Even numbers for which all divisors, with the exception of 1 and 2, are isolated. A positive divisor, k, of n is isolated if neither (k1) nor (k+1) divides n.


3



2, 4, 8, 10, 14, 16, 22, 26, 28, 32, 34, 38, 44, 46, 50, 52, 58, 62, 64, 68, 70, 74, 76, 82, 86, 88, 92, 94, 98, 104, 106, 116, 118, 122, 124, 128, 130, 134, 136, 142, 146, 148, 152, 154, 158, 164, 166, 170, 172, 176, 178, 184, 188, 190, 194, 196, 202, 206, 208, 212
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OFFSET

1,1


COMMENTS

Obviously, all divisors of an odd number are isolated.
a(n) = 2*A112886(n).  Chandler


LINKS

Table of n, a(n) for n=1..60.


EXAMPLE

28 is a term of the sequence because its divisors are 1,2,4,7,14, 28 and only 1 and 2 are nonisolated. 30 does not belong to the sequence because its divisors are 1,2,3,4,6,8,12, 24 and 1,2,3,4 are nonisolated.


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: a:=proc(n) if nops(b(n))= tau(n)2 then n else end if end proc: seq(a(n), n=4..200);


CROSSREFS

Cf. A112886, A133950, A133951, A088722A088726.
Sequence in context: A071703 A010069 A226872 * A125499 A240092 A153974
Adjacent sequences: A132892 A132893 A132894 * A132896 A132897 A132898


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Oct 16 2007, Oct 19 2007


EXTENSIONS

Corrected and extended by Ray Chandler, May 29 2008


STATUS

approved



