cp's OEIS Frontend

A380168 Nonsquares whose square part is greater than their squarefree part.

%I A380168 #9 Feb 10 2025 11:13:15
%S A380168 8,12,18,27,32,45,48,50,54,63,72,75,80,96,98,108,112,125,128,147,150,
%T A380168 160,162,175,176,180,192,200,208,216,224,240,242,243,245,250,252,275,
%U A380168 288,294,300,320,325,338,343,350,360,363,375,384,392,396,405,425,432,448
%N A380168 Nonsquares whose square part is greater than their squarefree part.
%C A380168 Numbers A000037(k) for which A007913(A000037(k)) < A008833(A000037(k)).
%H A380168 Felix Huber, <a href="/A380168/b380168.txt">Table of n, a(n) for n = 1..10000</a>
%e A380168 8 is in the sequence because its square part is 4 and its squarefree part is 2.
%e A380168 150 is in the sequence because its square part is 25 and its squarefree part is 6.
%p A380168 A380168:=proc(n)
%p A380168     option remember;
%p A380168     local a,r,i;
%p A380168     if n=1 then
%p A380168         8
%p A380168     else
%p A380168         for a from procname(n-1)+1 do
%p A380168             r:=1;
%p A380168             for i in ifactors(a)[2] do
%p A380168                 if is(i[2],odd) then
%p A380168                     r:=r*i[1]
%p A380168                 fi
%p A380168             od;
%p A380168             if r>1 and r<a/r then
%p A380168                 return a
%p A380168             fi
%p A380168         od
%p A380168     fi;
%p A380168 end proc;
%p A380168 seq(A380168(n),n=1..56);
%o A380168 (PARI) select(x->(x>sqr(core(x))), select(x->(!issquare(x)), [1..500])) \\ _Michel Marcus_, Feb 10 2025
%Y A380168 Cf. A000037, A000290, A007913, A008833, A056623.
%K A380168 nonn
%O A380168 1,1
%A A380168 _Felix Huber_, Jan 25 2025