A340691 Greatest image of A001222 over the prime indices of n.

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

Offset: 1

Author

Gus Wiseman, Jan 28 2021

Keywords

• nonn

Comments

For the initial term, we assume the empty set has maximum image 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

			The prime indices of 4070 are {1,3,5,12} -> {0,1,1,3}, so a(4070) = 3.
The prime indices of 8892 are {1,1,2,2,6,8} -> {0,0,1,1,2,3} so a(8892) = 3.
		

Crossrefs

Positions of first appearances are A033844.

Positions of 0's are A000079.

Positions of terms <= 1 are A302540.

Positions of 1's are A302540 \ A000079.

The version for minimum is A340928.

A003963 multiplies together the prime indices.

A056239 adds up the prime indices.

A061395 selects the greatest prime index.

A072233 counts partitions by sum and maximum.

A112798 lists the prime indices of each positive integer.

A303975 counts distinct prime factors in the product of prime indices.

Cf. A001222, A006530, A062447, A106529, A244990, A244991, A324522, A340606, A340609, A340610, A340856.

Programs

Mathematica

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