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A279787 Twice-partitioned numbers where the first partition is constant.

%I A279787 #18 Aug 27 2018 01:56:54
%S A279787 1,1,3,4,10,8,29,16,64,58,124,57,469,102,489,763,1597,298,3858,491,
%T A279787 8942,6355,6187,1256,59076,18766,20830,49694,167078,4566,481186,6843,
%U A279787 752128,362907,231592,1597802,5951007,21638,790404,2655810,25274798,44584,40898731
%N A279787 Twice-partitioned numbers where the first partition is constant.
%H A279787 Alois P. Heinz, <a href="/A279787/b279787.txt">Table of n, a(n) for n = 0..5723</a>
%H A279787 Gus Wiseman, <a href="/A279787/a279787.png">Illustration of the first 9 terms of A279787</a>
%H A279787 Gus Wiseman, <a href="/A063834/a063834.txt">Sequences enumerating triangles of integer partitions</a>
%F A279787 a(n) = Sum_{d|n} A000041(n/d)^d for n > 0. - _Andrew Howroyd_, Aug 26 2018
%e A279787 The a(4)=10 twice-partitions are:
%e A279787 ((4)), ((31)), ((22)), ((211)), ((1111)),
%e A279787 ((2)(2)), ((2)(11)), ((11)(2)), ((11)(11)),
%e A279787 ((1)(1)(1)(1)).
%p A279787 with(numtheory): with(combinat):
%p A279787 a:= proc(n) option remember; `if`(n=0, 1,
%p A279787       add(numbpart(n/d)^d, d=divisors(n)))
%p A279787     end:
%p A279787 seq(a(n), n=0..70);  # _Alois P. Heinz_, Dec 20 2016
%t A279787 nn=20;Table[DivisorSum[n,Power[PartitionsP[#],n/#]&],{n,nn}]
%o A279787 (PARI) a(n)=if(n==0, 1, sumdiv(n, d, numbpart(n/d)^d)) \\ _Andrew Howroyd_, Aug 26 2018
%Y A279787 Cf. A000005, A000041, A018818, A063834, A260685, A271619.
%K A279787 nonn
%O A279787 0,3
%A A279787 _Gus Wiseman_, Dec 18 2016