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 A083162 a(n) is the smallest unused proper divisor or proper multiple of n such that a(n)/n != a(m)/m for all m < n. 0
 2, 1, 9, 16, 25, 36, 49, 64, 3, 90, 110, 132, 156, 182, 210, 4, 255, 288, 323, 360, 399, 440, 483, 528, 5, 598, 648, 700, 754, 810, 868, 928, 990, 1054, 1120, 6, 1221, 1292, 1365, 1440, 1517, 1596, 1677, 1760, 1845, 1932, 2021, 2112, 7, 2250, 2346, 2444, 2544 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Previous name: a(n) is either a multiple or a divisor of n but not equal to n, such that a(n)/n = a(m)/m implies m = n and n/a(n)= m/a(m) also implies n = m. Also a(m) = a(n) if and only if m = n. Equivalently, a(n) is the smallest integer k other than n that is a divisor or multiple of n such that k/n != a(m)/m for all m < n. LINKS Table of n, a(n) for n=1..53. FORMULA a(a(n)) = n; a(n) = (b(k)/(k + 1)) if n = b(k) for some k and a(n) = n*(n - max{k: b(k) < n} + 1) otherwise, where b(k) is the k-th number at which a(n) < n. (Equivalently, b(k) is the unique x for which a(x)/x = (k+1).) - Carl B. Carlson (carlsonc(AT)stolaf.edu), Jan 09 2005 EXAMPLE a(3) = 9, a(3)/3 = 3 hence for no other m > 3, a(m) = 3m. a(1000) = 1000*(1000-max{k: b(k) < 1000} + 1) = 1000*(1000-29+1) = 972000. CROSSREFS A022342 gives the sequence analogous to b(n) if we replace the multiplications in the definition by additions. Sequence in context: A199887 A058876 A214884 * A178075 A221756 A094633 Adjacent sequences: A083159 A083160 A083161 * A083163 A083164 A083165 KEYWORD nonn AUTHOR Amarnath Murthy, Apr 25 2003 EXTENSIONS More terms from Carl B. Carlson (carlsonc(AT)stolaf.edu), Jan 09 2005 Edited and more terms added, Jon E. Schoenfield, Feb 21 2021 STATUS approved

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Last modified September 26 03:54 EDT 2023. Contains 365650 sequences. (Running on oeis4.)