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

%I #5 Mar 30 2019 08:36:50

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

%T 3,4,2,2,3,5,3,3,3,4,4,3,4,5,2,5,4,4,1,4,4,4,2,3,2,5,2,4,3,6,4,4,3,5,

%U 3,4,2,5,3,3,5,3,3,4,3,6,4,4,4,4,5,4,3

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

%C The sum of binary digits of an integer is the number of 1's 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)) = A000120(n).

%t Table[Sum[pr[[2]]*DigitCount[PrimePi[pr[[1]]],2,1],{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, A325120, A325122.

%K nonn

%O 1,4

%A _Gus Wiseman_, Mar 29 2019