# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a372497 Showing 1-1 of 1 %I A372497 #34 May 04 2024 15:13:01 %S A372497 24,120,360,840,960,1680,3024,4224,5040,7920,11880,17160,22800,24024, %T A372497 32760,36480,43680,57120,70224,73440,83520,93024,116280,121800,143640, %U A372497 175560,201600,212520,241080,255024,303600,330624,358800,421200,491400,570024,591360 %N A372497 Positive integers of the form k^2 - 1 that are the product of two other positive integers of the form k^2 - 1. %C A372497 This sequence is the sequence of possible c^2 - 1 values of all triples (a,b,c) of integers > 1 such that (a^2 - 1)*(b^2 - 1) = c^2 - 1. %H A372497 David A. Corneth, Table of n, a(n) for n = 1..19120 (first 408 terms from Ely Golden, terms <= 10^17) %H A372497 David A. Corneth, PARI program %e A372497 120 is a term since 120 = 15*8 = (4^2 - 1)*(3^2 - 1) and 120 = 11^2 - 1. %o A372497 (Python) %o A372497 from math import isqrt %o A372497 def is_perfect_square(n): return isqrt(abs(n))**2 == n %o A372497 limit = 10**17 %o A372497 sequence_entries = set() %o A372497 for a in range(2, isqrt(isqrt(limit))+1): %o A372497 u = a**2 - 1 %o A372497 for b in range(a+1, isqrt(limit//u+1)+1): %o A372497 v = b**2 - 1 %o A372497 if(is_perfect_square(u*v + 1)): sequence_entries.add(u*v) %o A372497 sequence_entries = sorted(sequence_entries) %o A372497 for i, j in enumerate(sequence_entries, 1): %o A372497 print(i, j) %o A372497 (PARI) isok1(k) = issquare(k+1); %o A372497 isok2(k) = fordiv(k, d, if (isok1(d) && isok1(k/d), return(1))); %o A372497 isok(k) = isok1(k) && isok2(k); \\ _Michel Marcus_, May 04 2024 %Y A372497 Intersection of A005563 and A063066. %K A372497 nonn %O A372497 1,1 %A A372497 _Ely Golden_, May 03 2024 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE