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A306213 Numbers that are the sum of cubes of three distinct positive integers in arithmetic progression. 2
36, 99, 153, 216, 288, 405, 408, 495, 645, 684, 792, 855, 972, 1071, 1197, 1224, 1407, 1548, 1584, 1701, 1728, 1968, 2079, 2241, 2304, 2403, 2541, 2673, 2736, 3051, 3060, 3240, 3264, 3537, 3540, 3888, 3960, 4059, 4131, 4257, 4500, 4587, 4833, 5049, 5160, 5256, 5472, 5643, 5832, 5940, 6336, 6369, 6669 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

153 = 1^3 + 3^3 + 5^3, with 3 - 1 = 5 - 3 = 2;

972 = 3^3 + 6^3 + 9^3, with 6 - 3 = 9 - 6 = 3.

PROG

(PARI) for(n=3, 7000, k=(n/3)^(1/3); a=2; v=0; while(a<=k&&v==0, b=(n-3*a^3)/(6*a); if(b==truncate(b)&&issquare(b), d=sqrt(b), d=0); if(d>=1&&d<=a-1, v=1; print1(n, ", ")); a+=1))

(PARI) w=List(); for(n=3, 7000, k=(n/3)^(1/3); for(a=2, k, for(c=1, a-1, v=(a-c)^3+a^3+(a+c)^3; if(v==n, listput(w, n))))); print(vecsort(Vec(w), , 8))

CROSSREFS

Cf. A000578, A023042, A024975, A122723, A306212, A306214.

Sequence in context: A287613 A118632 A260007 * A114819 A137945 A250812

Adjacent sequences:  A306210 A306211 A306212 * A306214 A306215 A306216

KEYWORD

nonn

AUTHOR

Antonio Roldán, Jan 29 2019

STATUS

approved

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Last modified July 20 01:17 EDT 2019. Contains 325168 sequences. (Running on oeis4.)