A327512 Maximum divisor of n that is 1, 2, or a nonprime number whose prime indices are pairwise coprime.

1, 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, 12, 1, 14, 15, 16, 1, 6, 1, 20, 1, 22, 1, 24, 1, 26, 1, 28, 1, 30, 1, 32, 33, 34, 35, 12, 1, 38, 1, 40, 1, 14, 1, 44, 15, 46, 1, 48, 1, 10, 51, 52, 1, 6, 55, 56, 1, 58, 1, 60, 1, 62, 1, 64, 1, 66, 1, 68, 69, 70, 1, 24, 1, 74

Offset: 1

Author

Gus Wiseman, Sep 19 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. Numbers that are 1, 2, or a nonprime number whose prime indices are pairwise coprime are listed in A302696, which is the union of this sequence.

a(n) is the greatest term of A302696 which divides n. - Antti Karttunen, Dec 06 2021

Examples

			The divisors of 72 that are 1, 2, or nonprime numbers whose prime indices are pairwise coprime are: {1, 2, 4, 6, 8, 12, 24}, so a(72) = 24.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Gus Wiseman, Sequences counting and encoding certain classes of multisets
• Index entries for sequences computed from indices in prime factorization

Crossrefs

See link for additional cross-references.

Cf. A000005, A006530, A056239, A112798, A289509, A302569, A302696, A304711.

Programs

Mathematica

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

PARI

isA302696(n) = if(isprimepower(n),!(n%2), if(!issquarefree(n>>valuation(n,2)), 0, my(pis=apply(primepi,factor(n)[,1])); (lcm(pis)==factorback(pis))));
A327512(n) = vecmax(select(isA302696,divisors(n))); \\ Antti Karttunen, Dec 06 2021