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A328177
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a(n) is the minimal value of the expression d OR (n/d) where d runs through the divisors of n and OR denotes the bitwise OR operator.
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3
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1, 3, 3, 2, 5, 3, 7, 6, 3, 7, 11, 6, 13, 7, 7, 4, 17, 7, 19, 5, 7, 11, 23, 6, 5, 15, 11, 7, 29, 7, 31, 12, 11, 19, 7, 6, 37, 19, 15, 13, 41, 7, 43, 15, 13, 23, 47, 12, 7, 15, 19, 13, 53, 15, 15, 14, 19, 31, 59, 13, 61, 31, 15, 8, 13, 15, 67, 21, 23, 15, 71, 9
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n)^2 >= n with equality iff n is a square.
a(p) = p for any odd prime number p.
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EXAMPLE
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For n = 12:
- we have the following values:
d 12/d d OR (12/d)
-- ---- -----------
1 12 13
2 6 6
3 4 7
4 3 7
6 2 6
12 1 13
- hence a(12) = min({6, 7, 13}) = 6.
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MAPLE
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a:= n-> min(map(d-> Bits[Or](d, n/d), numtheory[divisors](n))):
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PROG
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(PARI) a(n) = vecmin(apply(d -> bitor(d, n/d), divisors(n)))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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