A327395 Quotient of n over the maximum connected divisor of n.

1, 1, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 3, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 6, 1, 16, 3, 2, 5, 4, 1, 2, 1, 8, 1, 2, 1, 4, 5, 2, 1, 16, 1, 2, 3, 4, 1, 2, 5, 8, 1, 2, 1, 12, 1, 2, 1, 32, 1, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 2, 1, 16, 1, 2, 1, 4, 5

Offset

1,4

Comments

Requires A305079(n) steps to reach 1, the only fixed point.

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.

Links

Table of n, a(n) for n=1..85.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

a(n) = n/A327076(n).

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]]]]]]]]];
maxcon[n_]:=Max[Select[Divisors[n], Length[zsm[primeMS[#]]]<=1&]];
Table[n/maxcon[n], {n, 100}]

Crossrefs

See link for additional crossrefs.

Positions of 1's are A305078.

Positions of 2's are 2 * A305078.

Cf. A000005, A304716, A304714, A305079, A327076.

Sequence in context: A067005 A230849 A135517 * A327404 A360112 A333570

Adjacent sequences: A327392 A327393 A327394 * A327396 A327397 A327398

Keyword

nonn

Author

Gus Wiseman, Sep 15 2019

Status

approved