cp's OEIS Frontend

A303280 Number of strict integer partitions of n whose parts have a common divisor other than 1.

%I A303280 #11 Apr 29 2018 18:53:35
%S A303280 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,
%T A303280 32,13,38,7,57,1,54,19,68,1,95,1,90,33,104,1,148,5,149,39,166,1,230,
%U A303280 14,226,55,256,1,360,1,340,82,390,20,527,1,513,105,609,1
%N A303280 Number of strict integer partitions of n whose parts have a common divisor other than 1.
%H A303280 Alois P. Heinz, <a href="/A303280/b303280.txt">Table of n, a(n) for n = 1..10000</a>
%F A303280 a(n) = -Sum_{d|n, d > 1} mu(d) * A000009(n/d).
%e A303280 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).
%p A303280 with(numtheory):
%p A303280 b:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A303280       `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)
%p A303280     end:
%p A303280 a:= n-> -add(mobius(d)*b(n/d), d=divisors(n) minus {1}):
%p A303280 seq(a(n), n=1..100);  # _Alois P. Heinz_, Apr 23 2018
%t A303280 Table[-Sum[MoebiusMu[d]*PartitionsQ[n/d],{d,Rest[Divisors[n]]}],{n,100}]
%Y A303280 Cf. A000009, A000837, A018783, A051424, A078374, A168532, A289508, A289509, A298748, A300486, A302698, A302796, A303138.
%K A303280 nonn
%O A303280 1,6
%A A303280 _Gus Wiseman_, Apr 20 2018