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Number of nonempty subsets of {1..n} whose elements have an even harmonic mean.
3

%I #25 Sep 30 2022 14:36:17

%S 0,1,1,2,2,7,7,8,8,9,9,16,16,17,27,28,28,55,55,106,110,111,111,216,

%T 216,217,217,634,634,1155,1155,1156,2286,2287,3749

%N Number of nonempty subsets of {1..n} whose elements have an even harmonic mean.

%F a(p) = a(p-1) for prime p > 2. - _Michael S. Branicky_, Sep 30 2022

%e a(11) = 9 subsets: {2}, {4}, {6}, {8}, {10}, {3, 6}, {1, 3, 6}, {3, 4, 6} and {1, 2, 3, 6}.

%o (Python)

%o from fractions import Fraction

%o from functools import lru_cache

%o def cond(s, c): h = c/s; return h.denominator == 1 and h.numerator&1 == 0

%o @lru_cache(maxsize=None)

%o def b(n, s, c):

%o if n == 0: return int (c > 0 and cond(s, c))

%o return b(n-1, s, c) + b(n-1, s+Fraction(1, n), c+1)

%o a = lambda n: b(n, 0, 0)

%o print([a(n) for n in range(1, 18)]) # _Michael S. Branicky_, Sep 29 2022

%Y Cf. A339453, A357356, A357411, A357414, A357416.

%K nonn,more

%O 1,4

%A _Ilya Gutkovskiy_, Sep 27 2022

%E a(24)-a(35) from _Michael S. Branicky_, Sep 30 2022