A324749 - OEIS

%I #5 Mar 16 2019 10:12:26

%S 1,1,1,1,2,1,3,4,3,4,6,6,8,11,10,14,14,19,21,26,28,35,38,44,50,60,65,

%T 79,88,98,113,131,144,165,185,211,234,268,297,334,374,420,470,525,584,

%U 649,727,801,902,998,1100,1220,1357,1500,1657,1833,2029,2220,2462

%N Number of strict integer partitions of n containing no part > 1 whose prime indices all belong to the partition.

%C 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 The a(0) = 1 through a(10) = 6 strict integer partitions:

%e   ()  (1)  (2)  (3)  (4)    (5)  (6)    (7)    (8)    (9)    (10)

%e                      (3,1)       (4,2)  (4,3)  (6,2)  (5,4)  (6,4)

%e                                  (5,1)  (5,2)  (7,1)  (6,3)  (7,3)

%e                                         (6,1)         (7,2)  (8,2)

%e                                                              (9,1)

%e                                                              (6,3,1)

%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&!MemberQ[#,k_/;SubsetQ[#,PrimePi/@First/@FactorInteger[k]]]&]],{n,0,30}]

%Y The subset version is A324738. The non-strict version is A324754. The Heinz number version is A324759. An infinite version is A324694.

%Y Cf. A000720, A001462, A007097, A074971, A078374, A112798, A276625, A290822, A305713.

%Y Cf. A324744, A324750, A324755, A324760.

%K nonn

%O 0,5

%A _Gus Wiseman_, Mar 15 2019