

A048927


Numbers that are the sum of 5 positive cubes in exactly 2 ways.


9



157, 220, 227, 246, 253, 260, 267, 279, 283, 286, 305, 316, 323, 342, 344, 361, 368, 377, 379, 384, 403, 410, 435, 440, 442, 468, 475, 487, 494, 501, 523, 530, 531, 549, 562, 568, 586, 592, 594, 595, 599, 602, 621, 625, 640, 647, 657, 658, 683, 703, 710
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OFFSET

1,1


COMMENTS

It appears that this sequence has 15416 terms, the last of which is 2243453.  Donovan Johnson, Jan 11 2013
From a(1) = 157 we see that c(n) = (number of ways n is the sum of 5 cubes) coincides with A010057 = characteristic function of cubes, up to n = 156. This sequence lists the numbers n for which c(n) = 2. See A003328 for c(n) > 0 and A048926 for c(n) = 1.  M. F. Hasler, Jan 04 2023


LINKS



MATHEMATICA

Select[ Range[ 1000], (test = Length[ Select[ PowersRepresentations[#, 5, 3], And @@ (Positive /@ #)& ] ] == 2; If[test, Print[#]]; test)& ](* JeanFrançois Alcover, Nov 09 2012 *)


PROG

(Python)
def ways (n, left = 5, last = 1):
a = last; a3 = a**3; c = 0
while a3 <= nleft+1:
if left > 1:
c += ways(na3, left1, a)
elif a3 == n:
c += 1
a += 1; a3 = a**3
return c
for n in range (1, 1000): # to print this sequence
if ways(n)==2: print(n, end=", ") # in Python2 use, e.g.: print n,
(PARI) (waycount(n, numcubes, imax)={if(numcubes==0, !n, sum(i=1, imax, waycount(ni^3, numcubes1, i)))}); isA048927(n)=(waycount(n, 5, floor(n^(1/3)))==2); \\ Michael B. Porter, Sep 27 2009


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

More terms from Walter Hofmann (walterh(AT)gmx.de), Jun 01 2000


STATUS

approved



