

A083162


a(n) is either a multiple or a divisor or a [is there a word missing here?] 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.


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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..36.


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.
Sequence in context: A199887 A058876 A214884 * A178075 A221756 A094633
Adjacent sequences: A083159 A083160 A083161 * A083163 A083164 A083165


KEYWORD

more,nonn,uned


AUTHOR

Amarnath Murthy, Apr 25 2003


EXTENSIONS

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


STATUS

approved



