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A357412 Number of nonempty subsets of {1..n} whose elements have an even harmonic mean.

%I A357412 #25 Sep 30 2022 14:36:17
%S A357412 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 A357412 216,217,217,634,634,1155,1155,1156,2286,2287,3749
%N A357412 Number of nonempty subsets of {1..n} whose elements have an even harmonic mean.
%F A357412 a(p) = a(p-1) for prime p > 2. - _Michael S. Branicky_, Sep 30 2022
%e A357412 a(11) = 9 subsets: {2}, {4}, {6}, {8}, {10}, {3, 6}, {1, 3, 6}, {3, 4, 6} and {1, 2, 3, 6}.
%o A357412 (Python)
%o A357412 from fractions import Fraction
%o A357412 from functools import lru_cache
%o A357412 def cond(s, c): h = c/s; return h.denominator == 1 and h.numerator&1 == 0
%o A357412 @lru_cache(maxsize=None)
%o A357412 def b(n, s, c):
%o A357412     if n == 0: return int (c > 0 and cond(s, c))
%o A357412     return b(n-1, s, c) + b(n-1, s+Fraction(1, n), c+1)
%o A357412 a = lambda n: b(n, 0, 0)
%o A357412 print([a(n) for n in range(1, 18)]) # _Michael S. Branicky_, Sep 29 2022
%Y A357412 Cf. A339453, A357356, A357411, A357414, A357416.
%K A357412 nonn,more
%O A357412 1,4
%A A357412 _Ilya Gutkovskiy_, Sep 27 2022
%E A357412 a(24)-a(35) from _Michael S. Branicky_, Sep 30 2022