login
A340691
Greatest image of A001222 over the prime indices of n.
4
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
1,7
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.
EXAMPLE
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.
MATHEMATICA
Table[If[n==1, 0, Max@@PrimeOmega/@PrimePi/@First/@FactorInteger[n]], {n, 100}]
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.
Sequence in context: A050332 A369258 A337930 * A216658 A214020 A029425
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 28 2021
STATUS
approved