A358102 Numbers of the form prime(w)*prime(x)*prime(y) with w >= x >= y such that 2w = 3x + 4y.

66, 153, 266, 609, 806, 1295, 1599, 1634, 2107, 3021, 3055, 3422, 5254, 5369, 5795, 5829, 7138, 8769, 9443, 9581, 10585, 10706, 12337, 12513, 13298, 16465, 16511, 16849, 17013, 18602, 21983, 22145, 23241, 23542, 26159, 29014, 29607, 29945, 30943, 32623, 32809

Offset

1,1

Comments

Also Heinz numbers of integer partitions (w,x,y) summing to n such that 2w = 3x + 4y, where the Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Links

Table of n, a(n) for n=1..41.

Example

The terms together with their prime indices begin:
     66: {1,2,5}
    153: {2,2,7}
    266: {1,4,8}
    609: {2,4,10}
    806: {1,6,11}
   1295: {3,4,12}
   1599: {2,6,13}
   1634: {1,8,14}
   2107: {4,4,14}
   3021: {2,8,16}
   3055: {3,6,15}
   3422: {1,10,17}
   5254: {1,12,20}
   5369: {4,6,17}
   5795: {3,8,18}
   5829: {2,10,19}
   7138: {1,14,23}
   8769: {2,12,22}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], PrimeOmega[#]==3&&2*primeMS[#][[-1]]==3*primeMS[#][[-2]]+4*primeMS[#][[-3]]&]

Crossrefs

The ordered version is A357489, apparently counted by A008676.

These partitions are counted by A357849.

A000040 lists the primes.

A000041 counts partitions, strict A000009.

A003963 multiplies prime indices.

A056239 adds up prime indices.

Cf. A000720, A001221, A001222, A215366, A296150, A318283.

Sequence in context: A044698 A122125 A278783 * A258966 A258959 A062035

Adjacent sequences: A358099 A358100 A358101 * A358103 A358104 A358105

Keyword

nonn

Author

Gus Wiseman, Nov 02 2022

Status

approved