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%I #11 May 30 2024 15:59:27
%S 1641000816,1773440487,2476486656,20129719792,26256013056,28375047792,
%T 39623786496,106509692016,132921066096,143648679447,200595419136,
%U 218247135232,322075516672,420096208896,454000764672,600908378112,631190070000,633980583936,877482798192,1025625510000,1108400304375
%N Positive integers that can be expressed in at least three ways as (x-y)*(x^3-y^3).
%H Chai Wah Wu, <a href="/A373001/b373001.txt">Table of n, a(n) for n = 1..352</a>
%e 1773440487 is here via 1773440487 = (2706 - 2697) * (2706^3 - 2697^3) = (417 - 354) * (417^3 - 354^3) = (211 - 22) * (211^3 - 22^3).
%o (PARI) is(n) = {
%o if(valuation(n, 3) == 1, return(0));
%o my(f = factor(n), cf = f, q, c, dc);
%o cf[,2]>>=1;
%o c = factorback(cf);
%o dc = divisors(c);
%o for(i = 1, #dc,
%o dc2 = dc[i]^2;
%o dk = n/dc2;
%o if(dk > dc2 && (dk - dc2)%3 == 0,
%o D = dc2 + 4*(dk - dc2)/3;
%o if(issquare(D, &sD) && denominator((-dc[i] + sD)/2) == 1,
%o q++
%o )
%o )
%o );
%o q >= 3
%o
%o }
%Y Cf. A352244.
%K nonn
%O 1,1
%A _David A. Corneth_, May 19 2024
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