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A303280 Number of strict integer partitions of n whose parts have a common divisor other than 1. 7
0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 5, 1, 5, 4, 6, 1, 10, 1, 11, 6, 12, 1, 19, 3, 18, 8, 23, 1, 36, 1, 32, 13, 38, 7, 57, 1, 54, 19, 68, 1, 95, 1, 90, 33, 104, 1, 148, 5, 149, 39, 166, 1, 230, 14, 226, 55, 256, 1, 360, 1, 340, 82, 390, 20, 527, 1, 513, 105, 609, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = -Sum_{d|n, d > 1} mu(d) * A000009(n/d).

EXAMPLE

The a(18) = 10 strict partitions are (18), (10,8), (12,6), (14,4), (15,3), (16,2), (8,6,4), (9,6,3), (10,6,2), (12,4,2).

MAPLE

with(numtheory):

b:= proc(n) option remember; `if`(n=0, 1, add(add(

      `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)

    end:

a:= n-> -add(mobius(d)*b(n/d), d=divisors(n) minus {1}):

seq(a(n), n=1..100);  # Alois P. Heinz, Apr 23 2018

MATHEMATICA

Table[-Sum[MoebiusMu[d]*PartitionsQ[n/d], {d, Rest[Divisors[n]]}], {n, 100}]

CROSSREFS

Cf. A000009, A000837, A018783, A051424, A078374, A168532, A289508, A289509, A298748, A300486, A302698, A302796, A303138.

Sequence in context: A133755 A070104 A131085 * A318717 A331887 A328220

Adjacent sequences:  A303277 A303278 A303279 * A303281 A303282 A303283

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 20 2018

STATUS

approved

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Last modified April 7 13:01 EDT 2020. Contains 333305 sequences. (Running on oeis4.)