A281981 a(n) = 4*Sum_{i=1..n-1} Sum_{j=1..m} floor((j*i)/n) - (m-1)*m*(n-1) where m is floor(sqrt(n)).

0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, 6, 0, 2, 4, 8, 0, 8, 0, 8, 4, 4, 0, 12, 8, 4, 4, 8, 0, 16, 0, 8, 4, 4, 8, 22, 0, 6, 8, 18, 0, 18, 0, 10, 16, 6, 0, 22, 12, 14, 8, 10, 0, 18, 8, 22, 8, 6, 0, 30, 0, 6, 20, 24, 8, 20, 0, 16, 8, 28, 0, 36, 0, 8, 16, 16, 12, 20, 0, 32

Offset

1,4

Comments

Tsangaris proves that a(n)=0 iff n is prime (or 1) and a(n)>0 iff n is composite.

Links

Table of n, a(n) for n=1..80.

Panayiotis G. Tsangaris, Prime numbers and cyclotomy, Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae 31 (2004) 3-10.

Prog

(PARI) a(n) = if(iscomposite(n), my(m = sqrtint(n)); 4*sum(i=1, n-1, sum(j=1, m, (j*i)\n)) - (m-1)*m*(n-1), 0)

Crossrefs

Sequence in context: A139036 A292129 A291970 * A159006 A291968 A226171

Adjacent sequences: A281978 A281979 A281980 * A281982 A281983 A281984

Keyword

nonn

Author

Michel Marcus, Feb 04 2017

Extensions

Edited by Robert Israel, Feb 07 2017

Status

approved