A328169 GCD of the prime indices of n, all plus 1.

0, 2, 3, 2, 4, 1, 5, 2, 3, 2, 6, 1, 7, 1, 1, 2, 8, 1, 9, 2, 1, 2, 10, 1, 4, 1, 3, 1, 11, 1, 12, 2, 3, 2, 1, 1, 13, 1, 1, 2, 14, 1, 15, 2, 1, 2, 16, 1, 5, 2, 1, 1, 17, 1, 2, 1, 3, 1, 18, 1, 19, 2, 1, 2, 1, 1, 20, 2, 1, 1, 21, 1, 22, 1, 1, 1, 1, 1, 23, 2, 3, 2

Offset: 1

Author

Gus Wiseman, Oct 09 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(4,8) = 4.
		

Crossrefs

Positions of 0's and 1's are A318981.

Positions of records (first appearances) appear to be A116974.

The GCD of the prime indices of n, all minus 1, is A328167(n).

The LCM of the prime indices of n, all plus 1, is A328219(n).

Partitions whose parts plus 1 are relatively prime are A318980.

Cf. A000837, A056239, A112798, A258409, A289508, A289509, A290103, A328168.

Programs

Mathematica

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

Formula

a(n) = A289508(A003961(n)).