A325122 Sum of binary digits of the prime indices of n, minus Omega(n).

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 0, 1, 2, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 1, 1, 3, 0, 0, 2, 2, 1, 0, 0, 2, 0, 0, 1, 1, 1, 1, 2, 0, 0, 2, 1, 2, 2, 1, 1, 1, 0, 2, 1, 2, 0, 1, 1, 2, 1, 0, 2, 3, 0, 3, 2, 1

Offset: 1

Author

Gus Wiseman, Mar 29 2019

Keywords

• nonn

Comments

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.

Crossrefs

Positions of zeros are A318400.

Cf. A000120, A018900, A019565, A048881, A051438, A070939, A112798.

Cf. A325103, A325104, A325106, A325118.

Other totally additive sequences: A056239, A302242, A318994, A318995, A325033, A325034, A325120, A325121.

Programs

Mathematica

Table[Sum[pr[[2]]*(DigitCount[PrimePi[pr[[1]]],2,1]-1),{pr,If[n==1,{},FactorInteger[n]]}],{n,100}]

Formula

Totally additive with a(prime(n)) = A048881(n).