A324751 Number of strict integer partitions of n containing no prime indices of the parts.

1, 1, 1, 1, 2, 1, 3, 3, 2, 4, 5, 5, 6, 8, 8, 12, 10, 14, 13, 18, 19, 26, 25, 30, 34, 39, 40, 51, 55, 60, 71, 77, 90, 97, 111, 123, 136, 153, 170, 179, 216, 230, 264, 282, 322, 345, 385, 423, 470, 513, 573, 629, 686, 755, 834, 910, 1005, 1095, 1194, 1303, 1433

Offset

0,5

Comments

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..60.

Example

The a(1) = 1 through a(13) = 8 strict integer partitions (A...D = 10...13):
  1   2   3   4    5   6    7    8    9    A    B     C     D
              31       42   43   71   54   64   65    75    76
                       51   52        63   73   83    84    85
                                      72   82   542   93    94
                                           91   731   A2    B2
                                                      B1    643
                                                            751
                                                            931

Mathematica

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Intersection[#, PrimePi/@First/@Join@@FactorInteger/@#]=={}&]], {n, 0, 30}]

Crossrefs

The subset version is A324741, with maximal case A324743. The non-strict version is A324756. The Heinz number version is A324758. An infinite version is A304360.

Cf. A000720, A001462, A007097, A074971, A078374, A112798, A276625, A290822, A305713, A306844, A324764.

Cf. A324695, A324742, A324748.

Sequence in context: A006642 A332435 A361744 * A210595 A094435 A133341

Adjacent sequences: A324748 A324749 A324750 * A324752 A324753 A324754

Keyword

nonn

Author

Gus Wiseman, Mar 16 2019

Status

approved