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Sum of binary lengths of the prime indices of n.
2

%I #6 Mar 30 2019 08:36:43

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

%T 5,6,4,5,5,5,4,6,4,5,6,5,4,6,6,5,5,5,5,7,5,6,6,5,5,6,5,5,7,6,5,6,5,5,

%U 6,6,5,7,5,5,6,6,6,6,5,6,8,5,5,7,5,5,6

%N Sum of binary lengths of the prime indices of n.

%C The binary length of n is the number of digits in its binary representation. 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 Totally additive with a(prime(n)) = A070939(n).

%t Table[Sum[pr[[2]]*IntegerLength[PrimePi[pr[[1]]],2],{pr,FactorInteger[n]}],{n,100}]

%Y Cf. A000120, A000720, A001222, A019565, A048881, A070939, A112798.

%Y Cf. A325103, A325104, A325106, A325118, A325119.

%Y Other totally additive sequences: A056239, A302242, A318994, A318995, A325033, A325034, A325121, A325122.

%K nonn

%O 1,3

%A _Gus Wiseman_, Mar 29 2019