A298262 Number of integer partitions of n using relatively prime non-divisors of n.

0, 0, 0, 0, 1, 0, 3, 1, 3, 2, 13, 1, 23, 7, 10, 8, 65, 5, 104, 11, 53, 53, 252, 8, 244, 124, 203, 67, 846, 22, 1237, 157, 636, 569, 1074, 51, 3659, 1140, 1827, 221, 7244, 236, 10086, 1162, 1844, 4169, 19195, 225, 17657, 2997

Offset: 1

Author

Gus Wiseman, Jan 15 2018

Keywords

• nonn

Examples

			The a(11) = 13 partitions: (65), (74), (83), (92), (443), (533), (542), (632), (722), (3332), (4322), (5222), (32222).
The a(14) = 7 partitions: (9 5), (11 3), (5 5 4), (6 5 3), (8 3 3), (4 4 3 3), (5 3 3 3).
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000041, A000837, A002577, A002865, A018818, A018819, A049820, A098743, A100953, A200745, A275870, A281116.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],And[GCD@@#===1,!Or@@(Divisible[n,#]&/@#)]&]],{n,50}]

PARI

\\ here b(n) is A098743.
b(n)={polcoef(1/prod(k=1, n, if(n%k, 1 - x^k, 1) + O(x*x^n)), n)}
a(n)={sumdiv(n, d, moebius(d)*b(n/d))} \\ Andrew Howroyd, Aug 29 2018

Formula

a(n) = Sum_{d|n} mu(n/d) * A098743(d).