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 A287247 Numbers whose sum of proper divisors is equal to 289697407994. 6
 300629385430, 331082751976, 348602203870, 539890623754, 552235683634, 556381352806, 556523967562, 557844696646, 562012970938, 569170200598, 569518766962, 573004430386, 574282506778, 575462269366, 576199620754, 577107726658, 577305647026, 577419601138 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The number 289697407994 is the 47th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function. There are exactly 123 elements in the sequence. In 2016, C. Pomerance proved that, for every e>0, the number of preimages is O_e(n^{2/3+e}). Conjecture: there exists a positive real number k such that the number of preimages of an even number n is O((log n)^k). LINKS Anton Mosunov, Table of n, a(n) for n = 1..123 C. Pomerance, The first function and its iterates, A Celebration of the Work of R. L. Graham, S. Butler, J. Cooper, and G. Hurlbert, eds., Cambridge U. Press, to appear. EXAMPLE a(1) = 300629385430, because it is the smallest number whose sum of proper divisors is equal to 289697407994: 1 + 2 + 5 + 10 + 11 + 22 + 55 + 110 + 2732994413 + 5465988826 + 13664972065 + 27329944130 + 30062938543 + 60125877086 + 150314692715 = 289697407994. CROSSREFS Cf. A001065, A283156, A283157, A287233, A287238, A287251, A287262. Sequence in context: A345864 A354070 A273936 * A172578 A172588 A172691 Adjacent sequences:  A287244 A287245 A287246 * A287248 A287249 A287250 KEYWORD fini,full,nonn AUTHOR Anton Mosunov, May 22 2017 STATUS approved

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Last modified June 26 13:24 EDT 2022. Contains 354883 sequences. (Running on oeis4.)