A340928 Least image of A001222 applied to the prime indices of n.

0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 4, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1

Offset: 1

Author

Gus Wiseman, Jan 28 2021

Keywords

• nonn

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.

Examples

			The prime indices of 4277 are {4,6,15} with images {2,2,2}, so a(4277) = 2.
The prime indices of 8303 are {8,8,9} with images {3,3,2}, so a(8303) = 2.
		

Crossrefs

Positions of 0's are A000079.

Positions of first appearances are A033844.

The version for maximum is A340691.

A003963 multiplies together the prime indices.

A026794 counts partitions by sum and minimum.

A056239 adds up the prime indices.

A061395 selects the greatest prime index.

A112798 lists the prime indices of each positive integer.

Cf. A001222, A004277, A039900, A062447, A302540, A303975, A324522, A340610.

Programs

Mathematica

Table[If[n==1,0,Min@@PrimeOmega/@PrimePi/@First/@FactorInteger[n]],{n,100}]