cp's OEIS Frontend

A324748 Number of strict integer partitions of n containing all prime indices of the parts.

%I A324748 #10 Aug 22 2019 08:23:49
%S A324748 1,1,0,1,0,1,1,1,0,2,1,2,3,2,2,4,3,4,3,5,6,9,8,7,8,11,12,13,15,17,22,
%T A324748 22,20,28,31,32,36,41,43,53,53,59,70,76,77,89,99,108,124,135,139,160,
%U A324748 172,188,209,229,243,274,298,315,353,391,417,457,496,538,588
%N A324748 Number of strict integer partitions of n containing all prime indices of the parts.
%C A324748 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A324748 The first 15 terms count the following integer partitions.
%e A324748    1: (1)
%e A324748    3: (2,1)
%e A324748    5: (4,1)
%e A324748    6: (3,2,1)
%e A324748    7: (4,2,1)
%e A324748    9: (8,1)
%e A324748    9: (6,2,1)
%e A324748   10: (4,3,2,1)
%e A324748   11: (8,2,1)
%e A324748   11: (5,3,2,1)
%e A324748   12: (9,2,1)
%e A324748   12: (7,4,1)
%e A324748   12: (6,3,2,1)
%e A324748   13: (8,4,1)
%e A324748   13: (6,4,2,1)
%e A324748   14: (8,3,2,1)
%e A324748   14: (7,4,2,1)
%e A324748   15: (12,2,1)
%e A324748   15: (9,3,2,1)
%e A324748   15: (8,4,2,1)
%e A324748   15: (5,4,3,2,1)
%e A324748 An example for n = 6 is (20,18,11,5,3,2,1), with prime indices:
%e A324748   20: {1,1,3}
%e A324748   18: {1,2,2}
%e A324748   11: {5}
%e A324748    5: {3}
%e A324748    3: {2}
%e A324748    2: {1}
%e A324748    1: {}
%e A324748 All of these prime indices {1,2,3,5} belong to the partition, as required.
%t A324748 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&SubsetQ[#,PrimePi/@First/@Join@@FactorInteger/@DeleteCases[#,1]]&]],{n,0,30}]
%Y A324748 The subset version is A324736. The non-strict version is A324753. The Heinz number version is A290822. An infinite version is A324698.
%Y A324748 Cf. A000720, A001462, A007097, A074971, A078374, A112798, A276625, A279861, A290689, A290760, A305713.
%Y A324748 Cf. A324697, A324737, A324751.
%K A324748 nonn
%O A324748 0,10
%A A324748 _Gus Wiseman_, Mar 15 2019