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

1,17

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.

Links

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

Formula

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

Mathematica

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

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.

Sequence in context: A089224 A344987 A359325 * A234578 A069859 A179317

Adjacent sequences: A325119 A325120 A325121 * A325123 A325124 A325125

Keyword

nonn

Author

Gus Wiseman, Mar 29 2019

Status

approved