A327537 Quotient of n over the maximum divisor of n that is 1, prime, or whose prime indices are relatively prime.

1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 1, 1, 1, 1, 1, 3

Offset: 1

Author

Gus Wiseman, Sep 17 2019

Keywords

• nonn

Comments

All terms are odd.

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, prime, or whose prime indices are relatively prime are A327534. The maximum divisor of n satisfying the same conditions is A327535(n).

Examples

			The divisors of 63 that are 1, prime, or whose prime indices are relatively prime are {1, 3, 7}, so a(63) = 63/7 = 9.
		

Links

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

Crossrefs

See link for additional cross-references.

Cf. A000005, A006530, A032742, A056239, A112798, A289509, A327407.

Programs

Mathematica

Table[n/Max[Select[Divisors[n],#==1||PrimeQ[#]||GCD@@PrimePi/@First/@FactorInteger[#]==1&]],{n,100}]

Formula

If n is in A327534, then a(n) = 1; otherwise a(n) = n/A006530(n) = A032742(n).