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

Author

Gus Wiseman, May 18 2019

Keywords

• nonn

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.

Examples

			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}
		

Crossrefs

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

Programs

Mathematica

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