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%I #9 Jan 30 2022 11:42:09
%S 0,0,0,1,1,2,2,4,2,5,4,6,4,7,5,10,5,8,6,11,8,13,6,12,7,13,9,15,8,16,
%T 10,17,10,14,10,20,11,14,10,23,10,22,12,21,15,20,8,21,12,23,18,24,11,
%U 20,15,30,18,21,8,28,14,21,18,32,16,34,16,22,15,28,14,33,14,22,20,31,18,32,15
%N Number of partitions of n into 4 summands a>=b>=c>=d>0 with integer a/b, b/c and c/d.
%H Seiichi Manyama, <a href="/A121895/b121895.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Sum_{d|n, d>1} A122935(d-1). - _Franklin T. Adams-Watters_, Sep 20 2006
%e a(36)=20 because there are 20 partitions of 36 in 4 summands a>=b>=c>=d>0 with integer a/b, b/c and c/d:
%e {33, 1, 1, 1}, {32, 2, 1, 1}, {30, 2, 2, 2}, {28, 4, 2, 2}, {27, 3, 3, 3}, {25, 5, 5, 1}, {24, 8, 2, 2}, {24, 6, 3, 3}, {24, 4, 4, 4}, {21, 7, 7, 1}, {20, 10, 5, 1}, {18, 6, 6, 6}, {17, 17, 1, 1}, {16, 16, 2, 2}, {16, 8, 8, 4}, {15, 15, 5, 1}, {15, 15, 3, 3}, {14, 14, 7, 1}, {12, 12, 6, 6}, {9, 9, 9, 9}.
%Y Cf. A026810 = number of partitions of n into exactly 4 parts.
%Y Column 4 of A122934.
%Y Cf. A049822, A003238.
%K nonn
%O 1,6
%A _Zak Seidov_, Sep 01 2006
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