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A323766 Dirichlet convolution of the integer partition numbers A000041 with the number of divisors function A000005.

%I A323766 #13 Jan 28 2019 07:37:49
%S A323766 1,1,4,5,12,9,25,17,42,39,64,58,132,103,173,200,303,299,491,492,756,
%T A323766 832,1122,1257,1858,1975,2646,3083,4057,4567,6118,6844,8913,10265,
%U A323766 12912,14931,19089,21639,27003,31397,38830,44585,55138,63263,77371,89585,108076
%N A323766 Dirichlet convolution of the integer partition numbers A000041 with the number of divisors function A000005.
%C A323766 Also the number of constant multiset partitions of constant multiset partitions of integer partitions of n.
%H A323766 Vaclav Kotesovec, <a href="/A323766/b323766.txt">Table of n, a(n) for n = 0..10000</a>
%F A323766 a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*n*sqrt(3)). - _Vaclav Kotesovec_, Jan 28 2019
%e A323766 The a(6) = 25 constant multiset partitions of constant multiset partitions of integer partitions of 6:
%e A323766   ((6))
%e A323766   ((52))
%e A323766   ((42))
%e A323766   ((33))
%e A323766   ((3)(3))
%e A323766   ((3))((3))
%e A323766   ((411))
%e A323766   ((321))
%e A323766   ((222))
%e A323766   ((2)(2)(2))
%e A323766   ((2))((2))((2))
%e A323766   ((3111))
%e A323766   ((2211))
%e A323766   ((21)(21))
%e A323766   ((21))((21))
%e A323766   ((21111))
%e A323766   ((111111))
%e A323766   ((111)(111))
%e A323766   ((11)(11)(11))
%e A323766   ((111))((111))
%e A323766   ((11))((11))((11))
%e A323766   ((1)(1)(1)(1)(1)(1))
%e A323766   ((1)(1)(1))((1)(1)(1))
%e A323766   ((1)(1))((1)(1))((1)(1))
%e A323766   ((1))((1))((1))((1))((1))((1))
%t A323766 Table[If[n==0,1,Sum[PartitionsP[d]*DivisorSigma[0,n/d],{d,Divisors[n]}]],{n,0,30}]
%o A323766 (PARI) a(n) = if (n==0, 1, sumdiv(n, d, numbpart(d)*numdiv(n/d))); \\ _Michel Marcus_, Jan 28 2019
%Y A323766 Cf. A000005, A000041, A000837, A001970, A034729, A047968, A306017, A319066, A323764, A323765, A323774.
%K A323766 nonn
%O A323766 0,3
%A A323766 _Gus Wiseman_, Jan 27 2019