OFFSET
1,1
COMMENTS
Prime numbers are excluded because are banal solutions: in fact for them min(pi)=max(pi)=pi and then the area is zero.
Any squarefree number with an odd number of prime factors which are symmetrically distributed around the central one is part of the sequence. For instance with n=53295 the prime factors are 3, 5, 11, 17, 19 and 3+8=11=19-8, 5+6=11=17-6.
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..1000
EXAMPLE
n=140. Prime factors: 2, 2, 5, 7: min(pi)=2, max(pi)=7. Polynomial to integrate from 2 to 7: (x-2)^2*(x-5)*(x-7)=x^4-16*x^3+87*x^2-188x+140. The resulting area is equal to zero.
MAPLE
with(numtheory);
P:=proc(i)
local a, b, c, d, k, m, m1, m2, n;
for k from 1 to i do
a:=ifactors(k)[2]; b:=nops(a); c:=op(a); d:=1;
if b>1 then
m1:=c[1, 1]; m2:=0;
for n from 1 to b do
for m from 1 to c[n][2] do d:=d*(x-c[n][1]); od;
if c[n, 1]<m1 then m1:=c[n, 1]; fi; if c[n, 1]>m2 then m2:=c[n, 1]; fi;
od;
if int(d, x=m1..m2)=0 then print(k); fi;
fi;
od;
end:
P(500000);
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Jan 05 2012
STATUS
approved