OFFSET
0,32
COMMENTS
Positions of terms greater than 1 are {31, 37, 41, 43, 46, 47, 49, ...}.
A partition with no two distinct parts relatively prime is said to be intersecting.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..400
FORMULA
a(n > 0) = A202425(n) + 1.
EXAMPLE
Examples:
a(31) = 2: a(46) = 2:
(15,10,6) (15,15,10,6)
(1^31) (1^46)
a(37) = 3: a(47) = 7:
(15,12,10) (20,15,12)
(15,10,6,6) (21,14,12)
(1^37) (20,15,6,6)
a(41) = 4: (21,14,6,6)
(20,15,6) (15,12,10,10)
(21,14,6) (15,10,10,6,6)
(15,10,10,6) (1^47)
(1^41) a(49) = 6:
a(43) = 4: (24,15,10)
(18,15,10) (18,15,10,6)
(15,12,10,6) (15,12,12,10)
(15,10,6,6,6) (15,12,10,6,6)
(1^43) (15,10,6,6,6,6)
(1^39)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], GCD@@#==1&&And[And@@(GCD[##]>1&)@@@Subsets[Union[#], {2}]]&]], {n, 0, 32}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 29 2019
STATUS
approved