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

1641000816, 1773440487, 2476486656, 20129719792, 26256013056, 28375047792, 39623786496, 106509692016, 132921066096, 143648679447, 200595419136, 218247135232, 322075516672, 420096208896, 454000764672, 600908378112, 631190070000, 633980583936, 877482798192, 1025625510000, 1108400304375

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..352

Example

1773440487 is here via 1773440487 = (2706 - 2697) * (2706^3 - 2697^3) = (417 - 354) * (417^3 - 354^3) = (211 - 22) * (211^3 - 22^3).

Prog

(PARI) is(n) = {
	if(valuation(n, 3) == 1, return(0));
	my(f = factor(n), cf = f, q, c, dc);
	cf[, 2]>>=1;
	c = factorback(cf);
	dc = divisors(c);
	for(i = 1, #dc,
		dc2 = dc[i]^2;
		dk = n/dc2;
		if(dk > dc2 && (dk - dc2)%3 == 0,
			D = dc2 + 4*(dk - dc2)/3;
			if(issquare(D, &sD) && denominator((-dc[i] + sD)/2) == 1,
				q++
			)
		)	
	);
	q >= 3
}

Crossrefs

Cf. A352244.

Sequence in context: A381697 A329463 A246250 * A126432 A186175 A202573

Adjacent sequences: A372998 A372999 A373000 * A373002 A373003 A373004

Keyword

nonn

Author

David A. Corneth, May 19 2024

Status

approved