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A373001 Positive integers that can be expressed in at least three ways as (x-y)*(x^3-y^3).

%I A373001 #14 Dec 27 2024 01:22:20
%S A373001 1641000816,1773440487,2476486656,20129719792,26256013056,28375047792,
%T A373001 39623786496,106509692016,132921066096,143648679447,200595419136,
%U A373001 218247135232,322075516672,420096208896,454000764672,600908378112,631190070000,633980583936,877482798192,1025625510000,1108400304375
%N A373001 Positive integers that can be expressed in at least three ways as (x-y)*(x^3-y^3).
%H A373001 Chai Wah Wu, <a href="/A373001/b373001.txt">Table of n, a(n) for n = 1..352</a>
%e A373001 1773440487 is here via 1773440487 = (2706 - 2697) * (2706^3 - 2697^3) = (417 - 354) * (417^3 - 354^3) = (211 - 22) * (211^3 - 22^3).
%o A373001 (PARI) is(n) = {
%o A373001 	if(valuation(n, 3) == 1, return(0));
%o A373001 	my(f = factor(n), cf = f, q, c, dc);
%o A373001 	cf[,2]>>=1;
%o A373001 	c = factorback(cf);
%o A373001 	dc = divisors(c);
%o A373001 	for(i = 1, #dc,
%o A373001 		dc2 = dc[i]^2;
%o A373001 		dk = n/dc2;
%o A373001 		if(dk > dc2 && (dk - dc2)%3 == 0,
%o A373001 			D = dc2 + 4*(dk - dc2)/3;
%o A373001 			if(issquare(D, &sD) && denominator((-dc[i] + sD)/2) == 1,
%o A373001 				q++
%o A373001 			)
%o A373001 		)	
%o A373001 	);
%o A373001 	q >= 3
%o A373001 }
%Y A373001 Cf. A352244.
%K A373001 nonn
%O A373001 1,1
%A A373001 _David A. Corneth_, May 19 2024