A324753 Number of integer partitions of n containing all prime indices of their parts.

1, 1, 1, 2, 2, 4, 5, 7, 8, 14, 16, 23, 29, 40, 49, 66, 81, 109, 133, 172, 211, 274, 332, 419, 511, 640, 775, 965, 1165, 1434, 1730, 2109, 2530, 3083, 3683, 4447, 5308, 6375, 7573, 9062, 10730, 12786, 15104, 17909, 21095, 24937, 29284, 34488, 40421, 47450

Offset

0,4

Comments

These could be described as transitive integer partitions.

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.

Links

Table of n, a(n) for n=0..49.

Example

The a(1) = 1 through a(8) = 8 integer partitions:
  (1)  (11)  (21)   (211)   (41)     (321)     (421)      (3221)
             (111)  (1111)  (221)    (411)     (2221)     (4211)
                            (2111)   (2211)    (3211)     (22211)
                            (11111)  (21111)   (4111)     (32111)
                                     (111111)  (22111)    (41111)
                                               (211111)   (221111)
                                               (1111111)  (2111111)
                                                          (11111111)

Mathematica

Table[Length[Select[IntegerPartitions[n], SubsetQ[#, PrimePi/@First/@Join@@FactorInteger/@DeleteCases[#, 1]]&]], {n, 0, 30}]

Crossrefs

The subset version is A324736. The strict case is A324748. The Heinz number version is A290822. An infinite version is A324698.

Cf. A000720, A000837, A001462, A007097, A051424, A112798, A276625, A279861, A290689, A290760.

Cf. A324697, A324737.

Sequence in context: A348552 A058678 A241410 * A283106 A030769 A030739

Adjacent sequences: A324750 A324751 A324752 * A324754 A324755 A324756

Keyword

nonn

Author

Gus Wiseman, Mar 16 2019

Status

approved