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A186885 Numbers n whose squares are the average of two distinct positive cubes. 1
6, 42, 48, 78, 147, 162, 196, 336, 384, 456, 624, 722, 750, 1050, 1134, 1176, 1296, 1342, 1568, 1573, 1674, 1694, 2028, 2058, 2106, 2366, 2387, 2450, 2522, 2646, 2688, 2899, 3072, 3087, 3211, 3648, 3698, 3969, 4374, 4992, 5250, 5292, 5550, 5776, 5915, 6000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Trivially, if n is here also 1000n is, e.g., both 6 and

6000 are here. Also, no prime numbers here.

In the table, 396 triples {n,a,b} are given for all n's up to 5*10^5.

LINKS

Table of n, a(n) for n=1..46.

Zak Seidov, Triples {n,a,b} for n's up to 5*10^5

FORMULA

n^2 is average of two cubes:  n^2 = (a^3+b^3)/2, 0<a<b.

EXAMPLE

6^2 = (2^3+4^3)/2, 42^2 = (11^3+13^3)/2, 147^2 = (7^3+35^3)/2.

MATHEMATICA

nn = 13552; lim = Floor[(2 nn^2)^(1/3)]; Sort[Reap[Do[num = (a^3 + b^3)/2; If[IntegerQ[num] && num <= nn^2 && IntegerQ[Sqrt[num]], Sow[Sqrt[num]]], {a, lim}, {b, a - 1}]][[2, 1]]]

CROSSREFS

Sequence in context: A249135 A117693 A153243 * A097253 A083938 A176308

Adjacent sequences:  A186882 A186883 A186884 * A186886 A186887 A186888

KEYWORD

nonn

AUTHOR

Zak Seidov, Feb 28 2011

STATUS

approved

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Last modified October 31 17:19 EDT 2014. Contains 248868 sequences.