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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
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.
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.
Sequence in context: A067005 A230849 A135517 * A327404 A360112 A333570
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 15 2019
STATUS
approved