A325363 Heinz numbers of integer partitions into nonzero triangular numbers A000217.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 29, 32, 40, 47, 50, 52, 58, 64, 65, 73, 80, 94, 100, 104, 107, 116, 125, 128, 130, 145, 146, 151, 160, 169, 188, 197, 200, 208, 214, 232, 235, 250, 256, 257, 260, 290, 292, 302, 317, 320, 325, 338, 365, 376, 377, 394, 397

Offset

1,2

Comments

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 A007294.

Links

Table of n, a(n) for n=1..58.

Example

The sequence of terms together with their prime indices begins:
    1: {}
    2: {1}
    4: {1,1}
    5: {3}
    8: {1,1,1}
   10: {1,3}
   13: {6}
   16: {1,1,1,1}
   20: {1,1,3}
   25: {3,3}
   26: {1,6}
   29: {10}
   32: {1,1,1,1,1}
   40: {1,1,1,3}
   47: {15}
   50: {1,3,3}
   52: {1,1,6}
   58: {1,10}
   64: {1,1,1,1,1,1}
   65: {3,6}

Mathematica

nn=1000;
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
trgs=Table[n*(n+1)/2, {n, Sqrt[2*PrimePi[nn]]}];
Select[Range[nn], SubsetQ[trgs, primeMS[#]]&]

Crossrefs

Cf. A000217, A007294, A056239, A112798, A240026, A325327, A325360, A325362, A325367, A325390, A325394, A325400.

Sequence in context: A337483 A239517 A231056 * A000549 A191985 A126026

Adjacent sequences: A325360 A325361 A325362 * A325364 A325365 A325366

Keyword

nonn

Author

Gus Wiseman, May 02 2019

Status

approved