A325120 Sum of binary lengths of the prime indices of n.

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, 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, 6, 6, 5, 7, 5, 5, 6, 6, 6, 6, 5, 6, 8, 5, 5, 7, 5, 5, 6

Offset: 1

Author

Gus Wiseman, Mar 29 2019

Keywords

• nonn

Comments

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.

Crossrefs

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

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

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

Programs

Mathematica

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

Formula

Totally additive with a(prime(n)) = A070939(n).