|
|
A317831
|
|
Numerators of rational valued sequence f whose Dirichlet convolution with itself yields A000203 (sigma, the sum of divisors).
|
|
8
|
|
|
1, 3, 2, 19, 3, 3, 4, 63, 9, 9, 6, 19, 7, 6, 6, 867, 9, 27, 10, 57, 8, 9, 12, 63, 11, 21, 11, 19, 15, 9, 16, 3069, 12, 27, 12, 171, 19, 15, 14, 189, 21, 12, 22, 57, 27, 18, 24, 867, 41, 33, 18, 133, 27, 33, 18, 63, 20, 45, 30, 57, 31, 24, 18, 22199, 21, 18, 34, 171, 24, 18, 36, 567, 37, 57, 22, 95, 24, 21, 40, 2601, 227, 63, 42, 19, 27, 33
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A000203(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
|
|
PROG
|
(PARI)
A317831perA317832(n) = if(1==n, n, (sigma(n)-sumdiv(n, d, if((d>1)&&(d<n), A317831perA317832(d)*A317831perA317832(n/d), 0)))/2);
A317831(n) = numerator(A317831perA317832(n));
|
|
CROSSREFS
|
Cf. A317832 (gives the denominators).
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|