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A136164 a(n) is the number of divisors of n that are each coprime to the previous or the following divisor of n. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 17 05:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)