A327076 Maximum divisor of n that is 1 or connected.

1, 2, 3, 2, 5, 3, 7, 2, 9, 5, 11, 3, 13, 7, 5, 2, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 5, 31, 2, 11, 17, 7, 9, 37, 19, 39, 5, 41, 21, 43, 11, 9, 23, 47, 3, 49, 25, 17, 13, 53, 27, 11, 7, 57, 29, 59, 5, 61, 31, 63, 2, 65, 11, 67, 17, 23, 7, 71, 9, 73

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, which is the union of this sequence without 1.

Also the maximum MM-number (A302242) of a connected subset of the multiset of multisets with MM-number n.

Links

Table of n, a(n) for n=1..73.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

If n is in A305078, then a(n) = n.

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
zsm[s_]:=With[{c=Select[Subsets[Range[Length[s]], {2}], GCD@@s[[#]]>1&]}, If[c=={}, s, zsm[Sort[Append[Delete[s, List/@c[[1]]], LCM@@s[[c[[1]]]]]]]]];
Table[Max[Select[Divisors[n], Length[zsm[primeMS[#]]]<=1&]], {n, 30}]

Crossrefs

Positions of prime numbers are A302569.

Connected numbers are A305078.

Cf. A007947, A056239, A112798, A286518, A302242, A304716, A305079, A322338, A322390, A322391.

Sequence in context: A164858 A192330 A320028 * A215041 A347241 A338668

Adjacent sequences: A327073 A327074 A327075 * A327077 A327078 A327079

Keyword

nonn

Author

Gus Wiseman, Sep 05 2019

Status

approved