|
|
A110412
|
|
Sum_{d<n is a divisor of n} tau(n-d).
|
|
2
|
|
|
0, 1, 2, 4, 3, 7, 4, 9, 8, 9, 4, 17, 6, 10, 14, 18, 5, 20, 6, 21, 16, 12, 4, 33, 14, 13, 18, 24, 6, 33, 8, 29, 18, 12, 18, 44, 9, 13, 17, 41, 8, 37, 8, 26, 39, 14, 4, 57, 18, 30, 20, 28, 6, 41, 20, 45, 20, 14, 4, 68, 12, 16, 40, 46, 25, 43, 8, 25, 18, 44, 8, 80, 12, 16, 42, 30, 22, 42, 8
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
It appears that a(n) > tau(n) for n >= 4.
|
|
EXAMPLE
|
a(9) = tau(9-1)+tau(9-3) = tau(8)+tau(6) = 4+4 = 8.
|
|
MAPLE
|
with(numtheory): a:=proc(n) local div: div:=divisors(n): sum(tau(n-div[j]), j=1..tau(n)-1): end: seq(a(n), n=2..90); # Emeric Deutsch, Aug 05 2005
|
|
MATHEMATICA
|
f[n_] := Plus @@ (DivisorSigma[0, n - # ] & /@ Most[Divisors[n]]); Table[ f[n], {n, 79}] (* Robert G. Wilson v, Aug 05 2005 *)
|
|
PROG
|
(PARI) a(n) = sumdiv(n, d, if (d<n, numdiv(n-d))); \\ Michel Marcus, Aug 20 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|