A327390 Number of connected divisors of n.

1, 2, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 4, 2, 3, 4, 3, 2, 3, 3, 3, 4, 3, 2, 4, 2, 2, 3, 3, 3, 4, 2, 3, 4, 3, 2, 5, 2, 3, 4, 3, 2, 3, 3, 4, 3, 3, 2, 5, 3, 3, 4, 3, 2, 4, 2, 3, 6, 2, 4, 4, 2, 3, 3, 4, 2, 4, 2, 3, 4, 3, 3, 5, 2, 3, 5, 3, 2, 5, 3, 3, 4

Offset

1,2

Comments

A number n with prime factorization n = prime(m_1)^s_1 * ... * prime(m_k)^s_k is connected if the simple labeled graph with vertex set {m_1,...,m_k} and edges between any two vertices with a common divisor greater than 1 is connected. Connected numbers are listed in A305078. The maximum connected divisor of n is A327076(n).

Links

Table of n, a(n) for n=1..87.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
zsm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[Less@@#, GCD@@s[[#]]]>1&]}, If[c=={}, s, zsm[Sort[Append[Delete[s, List/@c[[1]]], LCM@@s[[c[[1]]]]]]]]];
Table[Length[Select[Divisors[n], Length[zsm[primeMS[#]]]<=1&]], {n, 100}]

Crossrefs

See link for additional cross-references.

Cf. A000005, A001221, A033273, A286518, A304714, A304716.

Sequence in context: A259578 A266547 A127992 * A169989 A067595 A184721

Adjacent sequences: A327387 A327388 A327389 * A327391 A327392 A327393

Keyword

nonn

Author

Gus Wiseman, Sep 15 2019

Status

approved