This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A301900 Heinz numbers of strict non-knapsack partitions. Squarefree numbers such that more than one divisor has the same Heinz weight A056239(d). 12

%I

%S 30,70,154,165,210,273,286,330,390,442,462,510,546,561,570,595,646,

%T 690,714,741,770,858,870,874,910,930,1045,1110,1122,1155,1173,1190,

%U 1230,1254,1290,1326,1330,1334,1365,1410,1430,1482,1495,1590,1610,1653,1770

%N Heinz numbers of strict non-knapsack partitions. Squarefree numbers such that more than one divisor has the same Heinz weight A056239(d).

%C An integer partition is knapsack if every distinct submultiset has a different sum. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%F Complement of A005117 in A299702.

%e Sequence of strict non-knapsack partitions begins: (321), (431), (541), (532), (4321), (642), (651), (5321), (6321), (761), (5421), (7321), (6421), (752), (8321), (743), (871), (9321), (7421), (862), (5431), (6521).

%t wt[n_]:=If[n===1,0,Total[Cases[FactorInteger[n],{p_,k_}:>k*PrimePi[p]]]];

%t Select[Range[1000],SquareFreeQ[#]&&!UnsameQ@@wt/@Divisors[#]&]

%Y Cf. A000712, A005117, A056239, A108917, A112798, A122768, A275972, A276024, A284640, A296150, A299701, A299702, A299729, A301829, A301854, A301899.

%K nonn

%O 1,1

%A _Gus Wiseman_, Mar 28 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 12 09:36 EST 2019. Contains 329953 sequences. (Running on oeis4.)