OFFSET
1,1
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..1000
EXAMPLE
n=1001. Prime factors: 7, 11 and 13: min(pi)=7, max(pi)=13. Polynomial: (x-7)*(x-11)*(x-13)= x^3-31*x^2+311*x-1001. Integral: x^4/4-31/3*x^3+311/2*x^2-1001*x. The area from x=7 to x=13 is 36.
n=1005. Prime factors: 3, 5 and 67: min(pi)=3, max(pi)=67. Polynomial: (x-3)*(x-5)*(x-67)= x^3-75*x^2+551*x-1005. Integral: x^4/4-25*x^3+551/2*x^2-1005*x. The area from x=3 to x=67 is -1310720.
n=1470. Prime factors: 2, 3, 5 and 7^2: min(pi)=2, max(pi)=7. Polynomial: (x-2)*(x-3)*(x-5)*(x-7)^2= x^5-24*x^4+220*x^3-954*x^2+1939*x-1470. Integral: x^6/6-24/5*x^5+55*x^4-318*x^3+1939/2*x^2-1470*x. The area from x=3 to x=67 is 0.
MAPLE
isA245284 := proc(n)
local pfs, x1, x2, po, x ;
if isprime(n) then
false;
else
pfs := ifactors(n)[2] ;
if nops(pfs) > 1 then
x1 := A020639(n) ;
x2 := A006530(n) ;
po := mul((x-op(1, p))^op(2, p), p=pfs) ;
int(po, x=x1..x2) ;
type(%, 'integer') ;
else
false;
end if;
end if;
end proc:
for n from 4 to 600 do
if isA245284(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Sep 07 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Aug 22 2014
EXTENSIONS
Definition and example corrected by R. J. Mathar, Sep 07 2014
STATUS
approved