|
| |
|
|
A079124
|
|
Number of ways to partition n into distinct positive integers <= phi(n), where phi is Euler's totient function (A000010).
|
|
7
|
|
|
|
1, 1, 0, 1, 0, 2, 0, 4, 1, 5, 1, 11, 0, 17, 4, 13, 13, 37, 2, 53, 13, 51, 35, 103, 10, 135, 78, 167, 89, 255, 4, 339, 253, 378, 306, 542, 121, 759, 558, 872, 498, 1259, 121, 1609, 1180, 1677, 1665, 2589, 808, 3250, 1969, 3844, 3325, 5119, 1850, 6268, 4758, 7546, 7070
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,6
|
|
|
REFERENCES
|
Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem, Mathematics and Computer Education, Vol. 31, No. 1, pp. 24-28, Winter 1997. MathEduc Database (Zentralblatt MATH, 1997c.01891).
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = b(0, n), b(m, n) = 1 + sum(b(i, j): m<i<j<phi(n) & i+j=n).
|
|
|
MAPLE
|
with(numtheory):
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, b(n-i, i-1))))
end:
a:= n-> b(n, phi(n)):
|
|
|
MATHEMATICA
|
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, b[n-i, i-1]]]]; a[n_] := b[n, EulerPhi[n]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 30 2015, after Alois P. Heinz *)
|
|
|
PROG
|
(Haskell)
a079124 n = p [1 .. a000010 n] n where
p _ 0 = 1
p [] _ = 0
p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
