This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A340827 #25 Feb 26 2023 19:38:51
%S A340827 1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1,1,2,1,2,1,1,1,5,1,1,1,1,1,3,1,1,1,1,
%T A340827 1,5,1,1,1,3,1,2,1,1,1,1,1,6,1,1,1,1,1,2,1,1,1,1,1,25,1,1,1,1,1,2,1,1,
%U A340827 1,1,1,18,1,1,1,1,1,2,1,3,1,1,1,17,1,1,1,1,1,14,1,1,1,1,1,12,1,1,1,3,1,2,1,1,1
%N A340827 Number of strict integer partitions of n into divisors of n whose length also divides n.
%C A340827 The first element not in A326715 that is however a Heinz number of these partitions is 273.
%H A340827 David A. Corneth, <a href="/A340827/b340827.txt">Table of n, a(n) for n = 1..10000</a> (first 2519 terms from Antti Karttunen)
%H A340827 Antti Karttunen, <a href="/A340827/a340827.txt">Scheme program for computing this sequence</a>
%e A340827 The a(n) partitions for n = 6, 12, 24, 90, 84:
%e A340827 6 12 24 90 84
%e A340827 3,2,1 6,4,2 12,8,4 45,30,15 42,28,14
%e A340827 6,3,2,1 12,6,4,2 45,30,9,5,1 42,21,14,7
%e A340827 12,8,3,1 45,18,15,9,3 42,28,12,2
%e A340827 8,6,4,3,2,1 45,30,10,3,2 42,28,6,4,3,1
%e A340827 45,18,15,10,2 42,28,7,4,2,1
%e A340827 45,30,6,5,3,1 42,14,12,7,6,3
%e A340827 45,30,9,3,2,1 42,21,12,4,3,2
%e A340827 45,15,10,9,6,5 42,21,12,6,2,1
%e A340827 45,18,10,9,5,3 42,21,14,4,2,1
%e A340827 45,18,10,9,6,2 28,21,14,12,6,3
%e A340827 45,18,15,6,5,1 28,21,14,12,7,2
%e A340827 45,18,15,9,2,1 42,21,7,6,4,3,1
%e A340827 30,18,15,10,6,5,3,2,1 42,14,12,7,4,3,2
%e A340827 42,14,12,7,6,2,1
%e A340827 28,21,14,12,4,3,2
%e A340827 28,21,14,12,6,2,1
%t A340827 Table[Length[Select[IntegerPartitions[n,All,Divisors[n]],UnsameQ@@#&&Divisible[n,Length[#]]&]],{n,30}]
%o A340827 (PARI) A340827(n, divsleft=List(divisors(n)), rest=n, len=0) = if(rest<=0, !rest && !(n%len), my(s=0, d); forstep(i=#divsleft, 1, -1, d = divsleft[i]; listpop(divsleft,i); if(rest>=d, s += A340827(n, divsleft, rest-d, 1+len))); (s)); \\ _Antti Karttunen_, Feb 22 2023
%o A340827 (Scheme) ;; See the Links-section. - _Antti Karttunen_, Feb 22 2023
%Y A340827 Note: A-numbers of Heinz-number sequences are in parentheses below.
%Y A340827 The non-strict case is A326842 (A326847).
%Y A340827 A018818 = partitions using divisors (A326841).
%Y A340827 A047993 = balanced partitions (A106529).
%Y A340827 A067538 = partitions whose length/maximum divides sum (A316413/A326836).
%Y A340827 A072233 = partitions by sum and length, with strict case A008289.
%Y A340827 A102627 = strict partitions whose length divides sum.
%Y A340827 A326850 = strict partitions whose maximum part divides sum.
%Y A340827 A326851 = strict partitions w/ length and max dividing sum.
%Y A340827 A340828 = strict partitions w/ length divisible by max.
%Y A340827 A340829 = strict partitions w/ Heinz number divisible by sum.
%Y A340827 A340830 = strict partitions w/ parts divisible by length.
%Y A340827 Cf. A064173, A143773 (A316428), A168659, A326843 (A326837), A326852, A330950 (A324851), A340851, A340853.
%K A340827 nonn
%O A340827 1,6
%A A340827 _Gus Wiseman_, Feb 01 2021
%E A340827 Data section extended up to a(105) by _Antti Karttunen_, Feb 22 2023