A106265: Any comments and suggestions

[זקיר סעידוב - ד\"ר/Zakir Seidov Ph.D.]

	Dear SeqFans,
	just submitted A106265 (see below). 
	 
	My request to SEQGurus:
	Are there missing  numbers? 
	Is it known/correct/interesting...?
	Thanks,
	Zak
	 

		
		%I A106265
		%S A106265 2,4,7,11,13,15,18,19,20,23,25,26,28,35,39,40,44,45,47,48,49,53,54,55,56,60
		%N A106265 Numbers a such that equation Diophantine a+b^2=c^3 has integer solution(s) b and c.
		%C A106265 Relative (minimal) values of b and c: A106266, A106267:
		b=5,2,1,4,70,7,3,18,14,2,10,1,6,36,5,52,9,96,13,4,524,26,17,3,76,2
		c=3,2,2,3,17,4,3, 7, 6,3, 5,3,4,11,4,14,5,21, 6,4, 65, 9, 7,4,18,4
		Cf. A023055: (Apparently) differences between adjacent perfect powers 
		(integers of form a^b, a >= 1, b >= 2;
		A076438: n which appear to have a unique representation as the difference 
		of two perfect powers; that is, there is only one solution 
		to Pillai's equation a^x - b^y = n, with a>0, b>0, x>1, y>1;
		A076440: n which appear to have a unique representation as 
		the difference of two perfect powers and one of those powers is odd; 
		that is, there is only one solution to Pillai's equation a^x - b^y = n, 
		with a>0, b>0, x>1, y>1, 
		and that solution has odd x or odd y (or both odd); 
		A075772: Difference between n-th perfect power and the closest perfect power, etc.
		%F A106265 A106265(n) = [A106267(n)]^3-[A106266(n)]^2
		%Y A106265 A023055,A075772,A076438,A076440,A106266,A106267.
		%O A106265 1
		%K A106265 ,hard,more,nonn,unkn,
		%A A106265 Zak Seidov (zakseidov at yahoo.com), Apr 28 2005
		
		

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