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

1,3

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.

Links

Table of n, a(n) for n=1..87.

Formula

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

Mathematica

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

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.

Sequence in context: A196052 A080773 A134598 * A064515 A112754 A283467

Adjacent sequences: A325117 A325118 A325119 * A325121 A325122 A325123

Keyword

nonn

Author

Gus Wiseman, Mar 29 2019

Status

approved