

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
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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



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 kth 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*(1000max{k: b(k) < 1000} + 1) = 1000*(100029+1) = 972000.


CROSSREFS

A022342 gives the sequence analogous to b(n) if we replace the multiplications in the definition by additions.


KEYWORD

nonn


AUTHOR



EXTENSIONS

More terms from Carl B. Carlson (carlsonc(AT)stolaf.edu), Jan 09 2005


STATUS

approved



