A327536 Number of divisors of n that are 1, prime, or whose prime indices are relatively prime.

1, 2, 2, 3, 2, 4, 2, 4, 2, 4, 2, 6, 2, 4, 4, 5, 2, 5, 2, 6, 3, 4, 2, 8, 2, 4, 2, 6, 2, 8, 2, 6, 4, 4, 4, 8, 2, 4, 3, 8, 2, 7, 2, 6, 5, 4, 2, 10, 2, 5, 4, 6, 2, 6, 4, 8, 3, 4, 2, 12, 2, 4, 3, 7, 3, 8, 2, 6, 4, 8, 2, 11, 2, 4, 5, 6, 4, 7, 2, 10, 2, 4, 2, 11, 4

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 maximum divisor of n satisfying the same conditions is A327535(n).

Links

Table of n, a(n) for n=1..85.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Example

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

Mathematica

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

Crossrefs

See link for additional cross-references.

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

Sequence in context: A327391 A365207 A083903 * A341946 A339915 A306509

Adjacent sequences: A327533 A327534 A327535 * A327537 A327538 A327539

Keyword

nonn

Author

Gus Wiseman, Sep 17 2019

Status

approved