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 A300780 Pairs of numbers producing consecutive odd sums of divisors, i.e., sigma(a(2*k)) = sigma(a(2*k-1)) + 2, with sigma values given in A300779. 1
 1, 2, 9, 8, 36, 50, 241081, 117128, 15069924, 23011209, 95887457649, 92943436658, 31623999684484, 31716423048338, 48730521525625, 55647526914529, 202869088076944, 238595412613156, 316982950120225, 238595412613156, 12016309156631329, 9203885645879282 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS So far, a(2n-1) is always a square. Will this always hold? - M. F. Hasler, Mar 12 2018 LINKS EXAMPLE a(1) = 1, a(2) = 2 because sigma(2) - sigma(1) = 3 - 1 = 2. a(3) = 9, a(4) = 8 because sigma(8) - sigma(9) = 15 - 13 = 2. a(5) = 36, a(6) = 50 because sigma(50) - sigma(36) = 93 - 91 = 2. The first pairs have the following factorization: (3^2, 2*2^2), (6^2, 2*5^2), (491^2, 2*(2*11^2)^2), ((2*3*647)^2, (3^2*13*41)^2). - M. F. Hasler, Mar 12 2018 CROSSREFS Cf. A000203, A002191, A300779. Sequence in context: A215025 A162954 A129194 * A272347 A214300 A092397 Adjacent sequences:  A300777 A300778 A300779 * A300781 A300782 A300783 KEYWORD nonn,hard AUTHOR Hugo Pfoertner, Mar 12 2018 EXTENSIONS a(11)-a(22) from Giovanni Resta, Mar 13 2018 STATUS approved

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Last modified August 5 18:22 EDT 2021. Contains 346488 sequences. (Running on oeis4.)