This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A117582 #26 Oct 18 2022 01:25:45 %S A117582 0,2,5,10,15,24,34,46,57,74,90,114,141,174,208,244,287,334,387 %N A117582 The number of ratios t/(t-1), where t is a square number, which factor into primes less than or equal to prime(n). %C A117582 By a theorem of Størmer, the number of ratios m/(m-1) factoring into primes only up to p is finite. Some of these have square numerators. %C A117582 Equivalently, a(n) is the number of triples of consecutive prime(n)-smooth numbers. - _Lucas A. Brown_, Oct 04 2022 %H A117582 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/stormer.py">stormer.py</a>. %H A117582 E. F. Ecklund and R. B. Eggleton, <a href="http://www.jstor.org/stable/2317422">Prime factors of consecutive integers</a>, Amer. Math. Monthly, 79 (1972), 1082-1089. %H A117582 D. H. Lehmer, <a href="http://projecteuclid.org/euclid.ijm/1256067456">On a problem of Størmer</a>, Ill. J. Math., 8 (1964), 57-79. %H A117582 Wikipedia, <a href="http://en.wikipedia.org/wiki/Stormer%27s_theorem">Størmer's theorem</a> %e A117582 The ratios counted by a(3) are 4/3, 9/8, 16/15, 25/24, and 81/80. %e A117582 The ratios counted by a(4) are 4/3, 9/8, 16/15, 25/24, 36/35, 49/48, 64/63, 81/80, 225/224, and 2401/2400. %Y A117582 Cf. A002071, A117583. %K A117582 nonn,hard,more %O A117582 1,2 %A A117582 _Gene Ward Smith_, Apr 02 2006 %E A117582 Offset 1 and a(14)-a(18) by _Lucas A. Brown_, Oct 04 2022 %E A117582 a(19) from _Lucas A. Brown_, Oct 16 2022