login
This site is supported by donations to The OEIS Foundation.

 

Logo

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!)
A325364 Heinz numbers of integer partitions whose differences (with the last part taken to be zero) are weakly decreasing. 14

%I

%S 1,2,3,4,5,6,7,8,9,11,13,15,16,17,18,19,21,23,25,27,29,30,31,32,35,37,

%T 41,43,47,49,53,54,55,59,61,64,65,67,71,73,75,77,79,81,83,89,91,97,

%U 101,103,105,107,109,113,119,121,125,127,128,131,133,137,139

%N Heinz numbers of integer partitions whose differences (with the last part taken to be zero) are weakly decreasing.

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

%C The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (x, y, z) are (y - x, z - y). We adhere to this standard for integer partitions also even though they are always weakly decreasing. For example, the differences of (6,3,1) (with the last part taken to be 0) are (-3,-2,-1).

%C The enumeration of these partitions by sum is given by A320509.

%H Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>

%t primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];

%t Select[Range[100],GreaterEqual@@Differences[Append[primeptn[#],0]]&]

%Y Cf. A056239, A112798, A320348, A320466, A320509, A325327, A325361, A325364, A325367, A325389, A325390, A325397.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 02 2019

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 December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)