A317936 Numerators of sequence whose Dirichlet convolution with itself yields A100995 + A063524, that is, the characteristic function of A000961 (prime powers).

1, 1, 1, 7, 1, -1, 1, 17, 7, -1, 1, -5, 1, -1, -1, 139, 1, -5, 1, -5, -1, -1, 1, -5, 7, -1, 17, -5, 1, 3, 1, 263, -1, -1, -1, -31, 1, -1, -1, -5, 1, 3, 1, -5, -5, -1, 1, 19, 7, -5, -1, -5, 1, -5, -1, -5, -1, -1, 1, 9, 1, -1, -5, 995, -1, 3, 1, -5, -1, 3, 1, -53, 1, -1, -5, -5, -1, 3, 1, 19, 139, -1, 1, 9, -1, -1, -1, -5, 1, 9

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A100995(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

Prog

(PARI)
up_to = 65537;
DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u}; \\ From A317937.
v317936aux = DirSqrt(vector(up_to, n, if(1==n, 1, isprimepower(n))));
A317936(n) = numerator(v317936aux[n]);
for(n=1, up_to, write("b317936.txt", n, " ", A317936(n)));

Crossrefs

Cf. A000961, A100995, A046644 (denominators).

Cf. also A317939.

Sequence in context: A178637 A364092 A295294 * A277875 A357157 A317935

Adjacent sequences: A317933 A317934 A317935 * A317937 A317938 A317939

Keyword

sign,frac

Author

Antti Karttunen, Aug 14 2018

Status

approved