A328167 GCD of the prime indices of n, all minus 1.

0, 0, 1, 0, 2, 1, 3, 0, 1, 2, 4, 1, 5, 3, 1, 0, 6, 1, 7, 2, 1, 4, 8, 1, 2, 5, 1, 3, 9, 1, 10, 0, 1, 6, 1, 1, 11, 7, 1, 2, 12, 1, 13, 4, 1, 8, 14, 1, 3, 2, 1, 5, 15, 1, 2, 3, 1, 9, 16, 1, 17, 10, 1, 0, 1, 1, 18, 6, 1, 1, 19, 1, 20, 11, 1, 7, 1, 1, 21, 2, 1, 12

Offset: 1

Author

Gus Wiseman, Oct 08 2019

Keywords

• nonn

Comments

Zeros are ignored when computing GCD, and the empty set has GCD 0.

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.

Examples

			85 has prime indices {3,7}, so a(85) = GCD(2,6) = 2.
		

Crossrefs

Positions of 0's are A000079.

Positions of 1's are A328168.

Positions of records (first appearances) are A006005.

The GCD of the prime indices of n is A289508(n).

The GCD of the prime indices of n, all plus 1, is A328169(n).

Looking at divisors instead of prime indices gives A258409.

Partitions whose parts minus 1 are relatively prime are A328170.

Cf. A000837, A001222, A007359, A056239, A112798, A289509, A318978, A318981, A328163, A328164.

Programs

Mathematica

Table[GCD@@(PrimePi/@First/@If[n==1,{},FactorInteger[n]]-1),{n,100}]