[seqfan] Re: phi-partitions of n
Richard J. Mathar
mathar at mpia-hd.mpg.de
Thu Mar 9 19:18:05 CET 2017
In answer to http://list.seqfan.eu/pipermail/seqfan/2017-March/017348.html
A naive counting gives for "the number of phi-partitions of n" for n>=1
0,0,1,1,2,0,3,4,8,2,4,1,5,8,24,24,6,2,7,15,107,46,8,4,135,101,347,83,9
This uses the Jones' nomenclature where partitions must have at least
2 parts to count. Seems not be in the OEIS.
http://www.fq.math.ca/29-4.html
nophiofn := proc(n)
local a,k,phip ;
a := 0 ;
for k in combinat[partition](n) do
phip := add( numtheory[phi](p),p =k) ;
if phip = numtheory[phi](n) and nops(k) >1 then
a := a+1 ;
# print(n,k) ;
end if;
# print(n,k) ;
end do:
a ;
end proc:
for n from 1 to 30 do
printf("%d,",nophiofn(n)) ;
end do:
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