OFFSET
1,5
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: Sum_{d>=1} mu(d)*(-1 + 1/(Prod_{k>=2/d} 1 - x^(k*d - 1))). - Andrew Howroyd, Oct 17 2019
EXAMPLE
The a(7) = 9 partitions are (61), (43), (421), (4111), (322), (3211), (2221), (22111), (211111).
The a(8) = 13 partitions:
(62),
(332), (422), (431), (521), (611),
(3221), (4211),
(22211), (32111), (41111),
(221111),
(2111111).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], GCD@@(#+1)==1&]], {n, 30}]
PROG
(PARI) seq(n)={Vec(sum(d=1, n+1, moebius(d)*(-1 + 1/prod(k=ceil(2/d), (n+1)\d, 1 - x^(k*d-1) + O(x*x^n)))), -n)} \\ Andrew Howroyd, Oct 17 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 06 2018
STATUS
approved