A337319 -id:A337319 - cp's OEIS frontend

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

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Christoph B. Kassir, Mar 19 2021

nonn

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.)

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

Cf. A337319.

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

cp's OEIS Frontend

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.

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