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!)
 A296150 Triangle whose n-th row is the integer partition with Heinz number n. 150

%I

%S 1,2,1,1,3,2,1,4,1,1,1,2,2,3,1,5,2,1,1,6,4,1,3,2,1,1,1,1,7,2,2,1,8,3,

%T 1,1,4,2,5,1,9,2,1,1,1,3,3,6,1,2,2,2,4,1,1,10,3,2,1,11,1,1,1,1,1,5,2,

%U 7,1,4,3,2,2,1,1,12,8,1,6,2,3,1,1,1,13,4

%N Triangle whose n-th row is the integer partition with Heinz number n.

%C Same as A112798 with rows reversed. Row lengths are A001222. Rows sums are A056239.

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

%H Robert Israel, <a href="/A296150/b296150.txt">Table of n, a(n) for n = 1..10002</a> (rows 1 to 3272, flattened)

%e Sequence of partitions begins: (), (1), (2), (11), (3), (21), (4), (111), (22), (31), (5), (211), (6), (41), (32), (1111), (7), (221).

%p f := n -> op(map(numtheory:-pi, sort(map(`\$`@op, ifactors(n)[2]), `>`))):

%p map(f, [\$1..100]); # _Robert Israel_, Feb 09 2018

%t Table[If[n===1,{},Join@@Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]],{n,50}]

%Y Cf. A000041, A000720, A001222, A056239, A063834, A112798, A196545, A215366, A289501, A299200, A299201, A299202, A299203.

%K nonn,tabf,look

%O 1,2

%A _Gus Wiseman_, Feb 05 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 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)