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A357411
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Number of nonempty subsets of {1..n} whose elements have an odd harmonic mean.
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3
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1, 1, 2, 2, 3, 5, 6, 6, 7, 9, 10, 10, 11, 13, 26, 26, 27, 45, 46, 74, 93, 99, 100, 162, 163, 165, 166, 458, 459, 865, 866, 866, 1647, 1669, 2724
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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a(11) = 10 subsets: {1}, {3}, {5}, {7}, {9}, {11}, {2, 6}, {2, 3, 6}, {3, 6, 10} and {3, 5, 6, 10}.
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PROG
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(Python)
from fractions import Fraction
from functools import lru_cache
def cond(s, c): h = c/s; return h.denominator == 1 and h.numerator&1
@lru_cache(maxsize=None)
def b(n, s, c):
if n == 0: return int (c > 0 and cond(s, c))
return b(n-1, s, c) + b(n-1, s+Fraction(1, n), c+1)
a = lambda n: b(n, 0, 0)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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