A136164 a(n) is the number of divisors of n that are each coprime to the previous or the following divisor of n.

0, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 4, 2, 3, 3, 2, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 2, 4, 2, 5, 2, 2, 3, 3, 3, 4, 2, 3, 3, 5, 2, 5, 2, 4, 4, 3, 2, 4, 2, 3, 3, 4, 2, 3, 3, 5, 3, 3, 2, 6, 2, 3, 4, 2, 3, 5, 2, 4, 3, 5, 2, 6, 2, 3, 3, 4, 3, 5, 2, 5, 2, 3, 2, 7, 3, 3, 3, 4, 2, 7, 3, 4, 3, 3, 3, 4, 2, 3, 4, 4, 2, 5, 2, 4, 5

Offset

1,2

Links

Diana Mecum, Table of n, a(n) for n = 1..1000

Example

The divisors of 28 are 1,2,4,7,14,28. Among adjacent pairs of divisors, 1 and 2 are coprime and 4 and 7 are coprime. Therefore there are a(28) = 4 divisors (1,2,4,7) that are each next to another divisor that they are coprime to.

Mathematica

Table[Boole[n > 1] + Total@ Boole@ Map[AnyTrue[Partition[#, 2, 1], CoprimeQ @@ # &] &, Partition[Append[Divisors[n], n], 3, 1]], {n, 105}] (* Michael De Vlieger, Aug 19 2017 *)

Crossrefs

Cf. A136165, A136166, A136167.

Sequence in context: A324292 A196941 A062843 * A182860 A328830 A033947

Adjacent sequences: A136161 A136162 A136163 * A136165 A136166 A136167

Keyword

nonn

Author

Leroy Quet, Dec 17 2007

Extensions

More terms from Diana L. Mecum, Jul 11 2007, Jul 13 2008

Status

approved