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

1,5

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.

Links

Table of n, a(n) for n=1..82.

Example

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

Mathematica

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

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.

Sequence in context: A126206 A307744 A119709 * A253556 A252735 A120251

Adjacent sequences: A328164 A328165 A328166 * A328168 A328169 A328170

Keyword

nonn

Author

Gus Wiseman, Oct 08 2019

Status

approved