A342724 a(n) = Sum_{primes p <= 2n} of g(frac(n/p)), where g(t) = [0 if t = 0, -1 if 0 < t < 1/2, 1 if t >= 1/2], and where frac(x) denotes the fractional part.

1, 1, 2, 1, 3, 1, 1, 3, 4, 2, 5, 3, 4, 3, 2, 0, 4, 5, 5, 6, 5, 2, 5, 3, 4, 5, 5, 6, 9, 6, 5, 7, 10, 7, 9, 6, 6, 7, 9, 6, 7, 4, 6, 7, 6, 6, 9, 10, 10, 11, 10, 7, 12, 10, 9, 9, 8, 8, 11, 11, 11, 12, 12, 10, 13, 9, 11, 12, 11, 7, 9, 10, 13, 14, 13, 10, 12, 11, 10

Offset

1,3

Comments

The function a(n) is a measure of how many times n rounds up (assigned value +1), down (assigned value -1), or not at all (assigned value +0) when divided by incremental prime numbers (see below example.)

Links

Table of n, a(n) for n=1..79.

Example

For n = 4, a(4) = 0 + (-1) + 1 + 1 = 2.

Prog

(PARI)
g(t) = {if(t==0, 0, if(t<1/2, -1, 1))}
a(n) = {sum(i=1, primepi(2*n), g(frac(n/prime(i))))} \\ Andrew Howroyd, Mar 20 2021

Crossrefs

Cf. A337319.

Sequence in context: A256435 A367412 A279945 * A347046 A300322 A144220

Adjacent sequences: A342721 A342722 A342723 * A342725 A342726 A342727

Keyword

nonn

Author

Christoph B. Kassir, Mar 19 2021

Status

approved