|
| |
|
|
A101271
|
|
Number of partitions of n into 3 distinct and relatively prime parts.
|
|
1
| |
|
|
1, 1, 2, 3, 4, 5, 6, 8, 9, 12, 12, 16, 15, 21, 20, 26, 25, 33, 28, 40, 36, 45, 42, 56, 44, 65, 56, 70, 64, 84, 66, 96, 81, 100, 88, 120, 90, 133, 110, 132, 121, 161, 120, 175, 140, 176, 156, 208, 153, 220, 180, 222, 196, 261, 184, 280, 225, 270, 240, 312, 230, 341, 272
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 6,3
|
|
|
FORMULA
| G.f. for the number of partitions of n into m distinct and relatively prime parts is Sum(moebius(k)*x^(m*(m+1)/2*k)/Product(1-x^(i*k), i=1..m), k=1..infinity).
|
|
|
EXAMPLE
| For n=10 we have 4 such partitions: 1+2+7, 1+3+6, 1+4+5 and 2+3+5.
|
|
|
MAPLE
| m:=3: with(numtheory): g:=sum(mobius(k)*x^(m*(m+1)/2*k)/Product(1-x^(i*k), i=1..m), k=1..20): gser:=series(g, x=0, 80): seq(coeff(gser, x^n), n=6..77); (Deutsch)
|
|
|
CROSSREFS
| Cf. A023022-A023030, A000741-A000743, A023031-A023035.
Sequence in context: A177738 A134030 A100054 * A093110 A165707 A052063
Adjacent sequences: A101268 A101269 A101270 * A101272 A101273 A101274
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 19 2004
|
|
|
EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 31 2005
|
| |
|
|
