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 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). 2
 0, 2, 5, 10, 15, 24, 34, 46, 57, 74, 90, 114, 141, 174, 208, 244, 287, 334, 387 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. Equivalently, a(n) is the number of triples of consecutive prime(n)-smooth numbers. - Lucas A. Brown, Oct 04 2022 LINKS Table of n, a(n) for n=1..19. Lucas A. Brown, stormer.py. E. F. Ecklund and R. B. Eggleton, Prime factors of consecutive integers, Amer. Math. Monthly, 79 (1972), 1082-1089. D. H. Lehmer, On a problem of Størmer, Ill. J. Math., 8 (1964), 57-79. Wikipedia, Størmer's theorem EXAMPLE The ratios counted by a(3) are 4/3, 9/8, 16/15, 25/24, and 81/80. 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. CROSSREFS Cf. A002071, A117583. Sequence in context: A163059 A099738 A064513 * A002134 A243971 A062472 Adjacent sequences: A117579 A117580 A117581 * A117583 A117584 A117585 KEYWORD nonn,hard,more AUTHOR Gene Ward Smith, Apr 02 2006 EXTENSIONS Offset 1 and a(14)-a(18) by Lucas A. Brown, Oct 04 2022 a(19) from Lucas A. Brown, Oct 16 2022 STATUS approved

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Last modified June 25 04:03 EDT 2024. Contains 373697 sequences. (Running on oeis4.)