A372433 Binary weight (number of ones in binary expansion) of the n-th squarefree number.

1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 3, 4, 4, 5, 2, 2, 3, 3, 3, 4, 3, 3, 4, 4, 5, 4, 4, 5, 4, 4, 5, 5, 5, 2, 2, 3, 3, 3, 4, 3, 3, 4, 4, 5, 3, 4, 4, 4, 5, 4, 5, 5, 5, 6, 3, 4, 4, 5, 4, 4, 5, 5, 5, 6, 4, 4, 5, 5, 6, 5, 6, 7, 2, 2, 3, 3, 3, 3, 3, 4, 4

Offset

1,3

Links

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

MathOverflow, Are there primes of every Hamming weight?

Wikipedia, Hamming weight.

Formula

a(n) = A000120(A005117(n)).

a(n) + A372472(n) = A372475(n) = A070939(A005117(n)).

Mathematica

DigitCount[Select[Range[100], SquareFreeQ], 2, 1]

Crossrefs

Restriction of A000120 to A005117.

For prime instead of squarefree we have A014499, zeros A035103.

Counting zeros instead of ones gives A372472, cf. A023416, A372473.

For binary length instead of weight we have A372475.

A003714 lists numbers with no successive binary indices.

A030190 gives binary expansion, reversed A030308.

A048793 lists positions of ones in reversed binary expansion, sum A029931.

A145037 counts ones minus zeros in binary expansion, cf. A031443, A031444, A031448, A097110.

A371571 lists positions of zeros in binary expansion, sum A359359.

A371572 lists positions of ones in binary expansion, sum A230877.

A372515 lists positions of zeros in reversed binary expansion, sum A359400.

A372516 counts ones minus zeros in binary expansion of primes, cf. A177718, A177796, A372538, A372539.

Cf. A039004, A049093, A049094, A059015, A069010, A070939, A073642, A211997, A368494, A372474.

Sequence in context: A368869 A128330 A133801 * A181630 A112310 A350240

Adjacent sequences: A372430 A372431 A372432 * A372434 A372435 A372436

Keyword

nonn,base

Author

Gus Wiseman, May 04 2024

Status

approved