A327389 Maximum divisor of n that is prime or whose prime indices are pairwise coprime.

1, 2, 3, 4, 5, 6, 7, 8, 3, 10, 11, 12, 13, 14, 15, 16, 17, 6, 19, 20, 7, 22, 23, 24, 5, 26, 3, 28, 29, 30, 31, 32, 33, 34, 35, 12, 37, 38, 13, 40, 41, 14, 43, 44, 15, 46, 47, 48, 7, 10, 51, 52, 53, 6, 55, 56, 19, 58, 59, 60, 61, 62, 7, 64, 13, 66, 67, 68, 69

Offset: 1

Author

Gus Wiseman, Sep 15 2019

Keywords

• nonn

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Links

• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

Cf. A000005, A000837, A006530, A056239, A112798, A327398.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Max[Select[Divisors[n],UnsameQ@@Sort[Join@@Union/@primeMS/@primeMS[#]]&]],{n,100}]

Formula

If n is in A302569, then a(n) = n.