|
|
A318650
|
|
Numerators of the sequence whose Dirichlet convolution with itself yields A057521, the powerful part of n.
|
|
1
|
|
|
1, 1, 1, 15, 1, 1, 1, 49, 35, 1, 1, 15, 1, 1, 1, 603, 1, 35, 1, 15, 1, 1, 1, 49, 99, 1, 181, 15, 1, 1, 1, 2023, 1, 1, 1, 525, 1, 1, 1, 49, 1, 1, 1, 15, 35, 1, 1, 603, 195, 99, 1, 15, 1, 181, 1, 49, 1, 1, 1, 15, 1, 1, 35, 14875, 1, 1, 1, 15, 1, 1, 1, 1715, 1, 1, 99, 15, 1, 1, 1, 603, 3235, 1, 1, 15, 1, 1, 1, 49, 1, 35, 1, 15, 1, 1, 1, 2023, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A057521(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
|
|
PROG
|
(PARI)
up_to = 65537;
A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); }; \\ From A057521
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};
v318650_aux = DirSqrt(vector(up_to, n, A057521(n)));
A318650(n) = numerator(v318650_aux[n]);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|