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!)
A316856 Heinz numbers of integer partitions whose reciprocal sum is an integer. 20

%I #7 Jul 15 2018 13:26:19

%S 1,2,4,8,9,16,18,32,36,64,72,81,125,128,144,147,162,195,250,256,288,

%T 294,324,390,500,512,576,588,648,729,780,1000,1024,1125,1152,1176,

%U 1296,1323,1458,1560,1755,2000,2048,2250,2304,2352,2401,2592,2646,2916,3120

%N Heinz numbers of integer partitions whose reciprocal sum is an integer.

%C The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.

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

%e 195 is the Heinz number of (6,3,2), which has reciprocal sum 1/6 + 1/3 + 1/2 = 1, which is an integer, so 195 belongs to the sequence.

%e The sequence of all integer partitions whose reciprocal sum is an integer begins: (), (1), (11), (111), (22), (1111), (221), (11111), (2211), (111111), (22111), (2222).

%t Select[Range[1000],IntegerQ[Sum[m[[2]]/PrimePi[m[[1]]],{m,If[#==1,{},FactorInteger[#]]}]]&]

%Y Cf. A000041, A051908, A056239, A058360, A072411, A296150, A316854, A316855, A316857.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jul 14 2018

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 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)