login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Positive integers with fewer non-isolated divisors than isolated divisors. A divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n. A divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.
2

%I #8 Apr 09 2014 10:16:33

%S 1,3,5,7,9,11,13,15,16,17,19,21,23,25,27,28,29,31,32,33,35,36,37,39,

%T 41,43,44,45,47,48,49,50,51,52,53,54,55,57,59,61,63,64,65,66,67,68,69,

%U 70,71,73,75,76,77,78,79,80,81,83,85,87,88,89,91,92,93,95,96,97,98,99,100

%N Positive integers with fewer non-isolated divisors than isolated divisors. A divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n. A divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.

%C All odd positive integers are in the sequence, since every divisor of any odd number is isolated.

%e The divisors of 50 are 1,2,5,10,25,50. Of these, 1 and 2 are non-isolated divisors and 5,10,25,50 are isolated divisors. There are fewer non-isolated divisors (2 in number) than isolated divisors (4 in number), so 50 is in the sequence.

%Y Cf. A134320, A134321.

%K nonn

%O 1,2

%A _Leroy Quet_, Oct 20 2007

%E Extended by _Ray Chandler_, Jun 24 2008