A103156 - OEIS

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A103156

Numbers whose square can be expressed as signed sum of a fifth power and a cube. z^2=x^5+y^3 with gcd(x,y,z)=1.

3, 10, 411, 654, 7792, 36599, 39151, 647992, 1506463, 1525899, 2730128, 3353687, 4387861, 4942947, 5574720, 12092581, 128301258, 168454745, 184589480, 888155653, 20364997771, 53242416249, 65464918703, 73699708330, 74330984303 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	LINKS	`Dario Alpern, Sum of powers a^5 + b^3 = c^2.` `Johnny Edwards, A Complete Solution to X^2+Y^3+Z^5=0. Journal fuer die reine und angewandte Mathematik (Crelle's Journal) 571, 213-236 (2004) (Preprint).`
	EXAMPLE	`a(1)=3 because 1^5+2^3=3^2, a(2)=10 because (-3)^5+7^3=10^2, a(3)=411 because 10^5+41^3=411^2, a(4)=654 because 19^5+(-127)^3=654^2.`
	CROSSREFS	`Cf. A070065 positive integer solutions of x^2 + y^5 = z^3.` `Sequence in context: A156193 A119035 A004100 * A202712 A006273 A183130` `Adjacent sequences: A103153 A103154 A103155 * A103157 A103158 A103159`
	KEYWORD	`nonn`
	AUTHOR	`Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 25 2005`

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Last modified February 14 01:35 EST 2012. Contains 205567 sequences.