A325777 Heinz numbers of integer partitions whose distinct consecutive subsequences do not have different sums.

12, 24, 30, 36, 40, 48, 60, 63, 70, 72, 80, 84, 90, 96, 108, 112, 120, 126, 132, 140, 144, 150, 154, 156, 160, 165, 168, 180, 189, 192, 198, 200, 204, 210, 216, 220, 224, 228, 240, 252, 264, 270, 273, 276, 280, 286, 288, 300, 308, 312, 315, 320, 324, 325, 330

Offset: 1

Author

Gus Wiseman, May 20 2019

Keywords

• nonn

Comments

First differs from A299729 in lacking 462.

This sequence does not contain all multiples of its elements. For example, it contains 154 (with prime indices {1,4,5}) but not 462 (with prime indices {1,2,4,5}).

Crossrefs

Complement of A325778.

Cf. A002033, A056239, A112798, A143823, A169942, A299702, A301899, A325676, A325683, A325768, A325769, A325770.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],!UnsameQ@@Total/@Union[ReplaceList[primeMS[#],{_,s__,_}:>{s}]]&]