login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325763 Heinz numbers of integer partitions whose consecutive subsequence-sums cover an initial interval of positive integers. 6
1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 48, 54, 56, 60, 64, 72, 80, 96, 100, 108, 112, 120, 128, 144, 160, 162, 168, 176, 180, 192, 200, 216, 224, 240, 256, 280, 288, 300, 320, 324, 336, 352, 360, 384, 392, 400, 416, 432, 448, 480, 486, 500, 504, 512 (list; graph; refs; listen; history; text; internal format)
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 appears to be A002865.
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
4: {1,1}
6: {1,2}
8: {1,1,1}
12: {1,1,2}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
24: {1,1,1,2}
32: {1,1,1,1,1}
36: {1,1,2,2}
40: {1,1,1,3}
48: {1,1,1,1,2}
54: {1,2,2,2}
56: {1,1,1,4}
60: {1,1,2,3}
64: {1,1,1,1,1,1}
72: {1,1,1,2,2}
80: {1,1,1,1,3}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Range[Total[primeMS[#]]]==Union[ReplaceList[primeMS[#], {___, s__, ___}:>Plus[s]]]&]
CROSSREFS
Sequence in context: A068563 A124240 A320580 * A363949 A068997 A293928
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 19 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 08:12 EDT 2024. Contains 371236 sequences. (Running on oeis4.)