A340691 - OEIS

%I #9 Jan 28 2021 17:01:08

%S 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,

%T 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,

%U 2,2,3,1,2,3,1,3,2,2,2,1,1,1,1,2,1,2,2,1

%N Greatest image of A001222 over the prime indices of n.

%C For the initial term, we assume the empty set has maximum image 0.

%C 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.

%e The prime indices of 4070 are {1,3,5,12} -> {0,1,1,3}, so a(4070) = 3.

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

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

%Y Positions of first appearances are A033844.

%Y Positions of 0's are A000079.

%Y Positions of terms <= 1 are A302540.

%Y Positions of 1's are A302540 \ A000079.

%Y The version for minimum is A340928.

%Y A003963 multiplies together the prime indices.

%Y A056239 adds up the prime indices.

%Y A061395 selects the greatest prime index.

%Y A072233 counts partitions by sum and maximum.

%Y A112798 lists the prime indices of each positive integer.

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

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

%K nonn

%O 1,7

%A _Gus Wiseman_, Jan 28 2021