A134322 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.

1, 3, 5, 7, 9, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 41, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 75, 76, 77, 78, 79, 80, 81, 83, 85, 87, 88, 89, 91, 92, 93, 95, 96, 97, 98, 99, 100

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..71.

Example

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.

Crossrefs

Cf. A134320, A134321.

Sequence in context: A293703 A120890 A321499 * A186328 A063460 A329831

Adjacent sequences: A134319 A134320 A134321 * A134323 A134324 A134325

Keyword

nonn

Author

Leroy Quet, Oct 20 2007

Extensions

Extended by Ray Chandler, Jun 24 2008

Status

approved