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

1,9

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).

Links

Table of n, a(n) for n=1..87.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

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

Example

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.

Mathematica

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

Crossrefs

See link for additional cross-references.

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

Sequence in context: A097031 A372565 A354997 * A120263 A250208 A325825

Adjacent sequences: A327534 A327535 A327536 * A327538 A327539 A327540

Keyword

nonn

Author

Gus Wiseman, Sep 17 2019

Status

approved