A327535 Maximum divisor of n that is 1, prime, or whose prime indices are relatively prime.

1, 2, 3, 4, 5, 6, 7, 8, 3, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 7, 22, 23, 24, 5, 26, 3, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 7, 50, 51, 52, 53, 54, 55, 56, 19, 58, 59, 60, 61, 62, 7, 64, 13, 66, 67, 68, 69

Offset

1,2

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, prime, or whose prime indices are relatively prime are A327534. The number of divisors of n satisfying the same conditions is A327536(n).

Links

Table of n, a(n) for n=1..69.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

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

Example

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

Mathematica

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

Crossrefs

See link for additional cross-references.

Cf. A000005, A000961, A006530, A056239, A112798, A281116, A289509, A327407.

Sequence in context: A160597 A327389 A282779 * A305902 A245350 A307282

Adjacent sequences: A327532 A327533 A327534 * A327536 A327537 A327538

Keyword

nonn

Author

Gus Wiseman, Sep 17 2019

Status

approved