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 A227054 a(n) = least triangular number t > 0 such that n*t is a triangular number, or 0 if no such t exists. 0
 1, 3, 1, 0, 3, 1, 3, 15, 0, 1, 6, 3, 6, 15, 1, 0, 78, 21, 10, 6, 1, 3, 45, 190, 0, 3, 55, 1, 15, 10, 15, 28203, 45, 105, 3, 1, 465, 120, 55, 3, 21, 15, 21, 3570, 1, 6, 210, 861, 0, 6, 3, 15, 105, 21945, 1, 21, 3, 66, 26565, 91, 276, 378, 6, 0, 1596, 1, 300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = 1 if and only if n is a triangular number. Indices of conjectured 0's: 4, 9, 16, 25, 49, 64, 81, 121, 144, 169, 225, 256, 289, 361, 400, 441, 529, 576, 625, 729, ... These are squares of 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27. a(n) = 0 if n = p^(2*j) where p is a prime and j > 0. - Jon E. Schoenfield, Sep 17 2023 LINKS Table of n, a(n) for n=1..67. EXAMPLE a(614) = 13964154294535688630985 = A000217(167117648945) because 614 * a(614) = A000217(4141012131555), and none of the smaller triangular numbers t satisfies 614*t = A000217(m) for some m. CROSSREFS Cf. A166478 (indices of t in A000217), A225502, A225503. Sequence in context: A058600 A133704 A160019 * A265605 A035629 A099546 Adjacent sequences: A227051 A227052 A227053 * A227055 A227056 A227057 KEYWORD nonn AUTHOR Alex Ratushnyak, Jun 29 2013 EXTENSIONS a(1)-a(25) and a(49)-a(67) from Jon E. Schoenfield, Sep 17 2023 STATUS approved

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Last modified August 13 01:30 EDT 2024. Contains 375113 sequences. (Running on oeis4.)