OFFSET
1,1
COMMENTS
Known terms are squares of A049575 or products of 2 distinct terms of A049575. - Michel Marcus, Jan 25 2023
This conjecture holds for terms <= 10^16. - David A. Corneth, Jan 25 2023
LINKS
David A. Corneth, Table of n, a(n) for n = 1..81
EXAMPLE
10 is in the sequence because 10 is a nonprime number and the proper divisors of 10 are 1, 2, 5, which are also partition numbers.
MAPLE
isA000041 := proc(n)
local k, P;
for k from 1 do
P := combinat[numbpart](k) ;
if P > n then
return false;
elif P = n then
return true ;
end if;
end do:
end proc:
isA236108 := proc(n)
local pdvs, d ;
if n =1 or isprime(n) then
return false;
end if;
pdvs := numtheory[divisors](n) minus {n} ;
for d in pdvs do
if not isA000041(d) then
return false;
end if;
end do:
return true;
end proc:
for n from 1 to 300000 do
if isA236108(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Jan 29 2014
MATHEMATICA
partitionNumbers = Table[PartitionsP[n], {n, 1, 1000}];
Select[Range[2, 10000],
If[! PrimeQ[#],
ContainsOnly[Divisors[#][[2 ;; -2]], partitionNumbers]] &] (* Julien Kluge, Dec 03 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jan 22 2014
EXTENSIONS
a(17)-a(26) from R. J. Mathar, Jan 29 2014
a(27)-a(32) from Jon E. Schoenfield, Feb 05 2014
a(33)-a(34) from Michel Marcus, Jan 24 2023
More terms from David A. Corneth, Jan 25 2023
STATUS
approved