A325762 Heinz numbers of integer partitions with no part greater than the number of ones.

1, 2, 4, 8, 12, 16, 24, 32, 36, 40, 48, 64, 72, 80, 96, 108, 112, 120, 128, 144, 160, 192, 200, 216, 224, 240, 256, 288, 320, 324, 336, 352, 360, 384, 400, 432, 448, 480, 512, 560, 576, 600, 640, 648, 672, 704, 720, 768, 784, 800, 832, 864, 896, 960, 972, 1000

Offset

1,2

Comments

After 1 and 2, first differs from A322136 in having 200.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

The enumeration of these partitions by sum is given by A002865.

Links

Table of n, a(n) for n=1..56.

Example

The sequence of terms together with their prime indices begins:
     1: {}
     2: {1}
     4: {1,1}
     8: {1,1,1}
    12: {1,1,2}
    16: {1,1,1,1}
    24: {1,1,1,2}
    32: {1,1,1,1,1}
    36: {1,1,2,2}
    40: {1,1,1,3}
    48: {1,1,1,1,2}
    64: {1,1,1,1,1,1}
    72: {1,1,1,2,2}
    80: {1,1,1,1,3}
    96: {1,1,1,1,1,2}
   108: {1,1,2,2,2}
   112: {1,1,1,1,4}
   120: {1,1,1,2,3}
   128: {1,1,1,1,1,1,1}
   144: {1,1,1,1,2,2}

Mathematica

Select[Range[100], #==1||EvenQ[#]&&PrimePi[FactorInteger[#][[-1, 1]]]<=FactorInteger[#][[1, 2]]&]

Crossrefs

Cf. A001222, A002865, A007814, A056239, A061395, A093641, A109298, A110295, A112798, A118914, A325761, A325763.

Sequence in context: A256941 A324174 A047836 * A231958 A227730 A246692

Adjacent sequences: A325759 A325760 A325761 * A325763 A325764 A325765

Keyword

nonn

Author

Gus Wiseman, May 18 2019

Status

approved