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A327395 Quotient of n over the maximum connected divisor of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A280726 A256607

Adjacent sequences:  A327392 A327393 A327394 * A327396 A327397 A327398

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 15 2019

STATUS

approved

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Last modified April 5 05:06 EDT 2020. Contains 333238 sequences. (Running on oeis4.)