[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


This uses the Jones' nomenclature where partitions must have at least
2 parts to count. Seems not be in the OEIS.

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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