cp's OEIS Frontend

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

%I A340691 #9 Jan 28 2021 17:01:08
%S A340691 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 A340691 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 A340691 2,2,3,1,2,3,1,3,2,2,2,1,1,1,1,2,1,2,2,1
%N A340691 Greatest image of A001222 over the prime indices of n.
%C A340691 For the initial term, we assume the empty set has maximum image 0.
%C A340691 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 A340691 The prime indices of 4070 are {1,3,5,12} -> {0,1,1,3}, so a(4070) = 3.
%e A340691 The prime indices of 8892 are {1,1,2,2,6,8} -> {0,0,1,1,2,3} so a(8892) = 3.
%t A340691 Table[If[n==1,0,Max@@PrimeOmega/@PrimePi/@First/@FactorInteger[n]],{n,100}]
%Y A340691 Positions of first appearances are A033844.
%Y A340691 Positions of 0's are A000079.
%Y A340691 Positions of terms <= 1 are A302540.
%Y A340691 Positions of 1's are A302540 \ A000079.
%Y A340691 The version for minimum is A340928.
%Y A340691 A003963 multiplies together the prime indices.
%Y A340691 A056239 adds up the prime indices.
%Y A340691 A061395 selects the greatest prime index.
%Y A340691 A072233 counts partitions by sum and maximum.
%Y A340691 A112798 lists the prime indices of each positive integer.
%Y A340691 A303975 counts distinct prime factors in the product of prime indices.
%Y A340691 Cf. A001222, A006530, A062447, A106529, A244990, A244991, A324522, A340606, A340609, A340610, A340856.
%K A340691 nonn
%O A340691 1,7
%A A340691 _Gus Wiseman_, Jan 28 2021