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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.
1
264, 308, 8192, 16400, 88508, 236684, 504812, 12127808, 22491308, 82310258, 227240552, 385278014, 1069061114, 2363758544, 2591166314, 2985365684, 3310448834, 4042988642, 4791339182, 5712714308, 7553782658, 8626601522, 12494656622, 14498688512, 15165306758, 15445891244
OFFSET
1,1
COMMENTS
Intersection of A253775, A254671, A255265.
LINKS
David A. Corneth, PARI program
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)]
(PARI) \\ See Corneth link
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Alex Ratushnyak, Mar 07 2015
EXTENSIONS
More terms from David A. Corneth, Oct 18 2024
STATUS
approved