login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326018 Heinz numbers of knapsack partitions such that no addition of one part up to the maximum is knapsack. 6
1925, 12155, 20995, 23375, 37145 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

An integer partition is knapsack if every submultiset has a different sum.

The enumeration of these partitions by sum is given by A326016.

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

The sequence of terms together with their prime indices begins:

   1925: {3,3,4,5}

  12155: {3,5,6,7}

  20995: {3,6,7,8}

  23375: {3,3,3,5,7}

  37145: {3,7,8,9}

MATHEMATICA

ksQ[y_]:=UnsameQ@@Total/@Union[Subsets[y]];

Select[Range[2, 200], With[{phm=If[#==1, {}, Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]}, ksQ[phm]&&Select[Table[Sort[Append[phm, i]], {i, Max@@phm}], ksQ]=={}]&]

CROSSREFS

Cf. A002033, A108917, A275972, A299702, A299729, A304793.

Cf. A325780, A325782, A325857, A325862, A325878, A325880, A326015, A326016.

Sequence in context: A107564 A135648 A255867 * A202051 A283949 A133301

Adjacent sequences:  A326015 A326016 A326017 * A326019 A326020 A326021

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 03 2019

STATUS

approved

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)