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

1,7

Links

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

Formula

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A112164 A300580 A075676 * A359525 A124814 A122567

Adjacent sequences: A298259 A298260 A298261 * A298263 A298264 A298265

Keyword

nonn

Author

Gus Wiseman, Jan 15 2018

Status

approved