A372442 - OEIS

%I #6 May 10 2024 08:50:29

%S 1,0,2,0,1,-1,3,2,1,-1,2,-2,0,1,4,-2,3,-3,2,1,0,-4,3,2,-1,3,1,-5,2,-6,

%T 5,1,-1,2,4,-6,-2,0,3,-7,2,-8,1,3,-3,-9,4,2,3,-1,0,-10,4,1,2,-2,-4,

%U -11,3,-12,-5,2,6,1,2,-12,0,-2,3,-13,5,-14,-5,4,-1

%N (Greatest binary index of n) minus (greatest prime index of n).

%C A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

%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.

%F a(n) = A070939(n) - A061395(n) = A029837(n) - A061395(n) for n > 1.

%t bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];

%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Table[Max[bix[n]]-Max[prix[n]],{n,2,100}]

%Y For sum instead of maximum we have A372428, zeros A372427.

%Y Positions of zeros are A372436.

%Y For minimum instead of maximum we have A372437, zeros {}.

%Y For length instead of maximum we have A372441, zeros A071814.

%Y Positions of odd terms are A372588, even A372589.

%Y A019565 gives Heinz number of binary indices, adjoint A048675.

%Y A029837 gives greatest binary index, least A001511.

%Y A048793 lists binary indices, length A000120, reverse A272020, sum A029931.

%Y A061395 gives greatest prime index, least A055396.

%Y A070939 gives length of binary expansion.

%Y A112798 lists prime indices, length A001222, reverse A296150, sum A056239.

%Y Cf. A000720, A003963, A014499, A174090, A243055, A355536, A359495, A372429-A372432, A372589-A372591.

%K sign,base

%O 2,3

%A _Gus Wiseman_, May 07 2024