A255804 Numbers representable as x*y*(x+y), b*c+b+c, and d^e+d+e, where d>1, e>1, b>=c>1 and x>=y>1.

264, 308, 8192, 16400, 88508, 236684, 504812, 12127808, 22491308, 82310258

Offset

1,1

Comments

Intersection of A253775, A254671, A255265.

Links

Table of n, a(n) for n=1..10.

Example

a(2) = 308 = 17^2 + 17 + 2 = 7 * 4 * (7 + 4) = 102 * 2 + 102 + 2.

Prog

(Python 2)
TOP = 100000000
a = [0]*TOP
c = []
for y in range(2, TOP/2):
  if 2**y + 2 + y >= TOP: break
for x in range(2, TOP/2):
    k = x**y+(x+y)
    if k>=TOP: break
    c.append(k)
for y in range(2, TOP/2):
  if 2*y*y*y >= TOP: break
for x in range(y, TOP/2):
    k = x*y*(x+y)
    if k>=TOP: break
    a[k]=1
for y in range(2, TOP/2):
  if y*(y+2) >= TOP: break
for x in range(y, TOP/2):
    k = x*y+(x+y)
    if k>=TOP: break
    a[k]|=2
    if a[k]==3 and (k in c): print k,
print [n for n in range(TOP) if a[n]==3 and (n in c)]

Crossrefs

Cf. A255267, A254034, A255265, A254671, A253775.

Sequence in context: A345844 A253694 A253701 * A351802 A050240 A105683

Adjacent sequences: A255801 A255802 A255803 * A255805 A255806 A255807

Keyword

nonn,more

Author

Alex Ratushnyak, Mar 07 2015

Status

approved