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A357411 Number of nonempty subsets of {1..n} whose elements have an odd harmonic mean.

%I A357411 #25 Sep 30 2022 14:37:07
%S A357411 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,
%T A357411 165,166,458,459,865,866,866,1647,1669,2724
%N A357411 Number of nonempty subsets of {1..n} whose elements have an odd harmonic mean.
%F A357411 a(p) = a(p-1) + 1 for prime p > 2. - _Michael S. Branicky_, Sep 30 2022
%e A357411 a(11) = 10 subsets: {1}, {3}, {5}, {7}, {9}, {11}, {2, 6}, {2, 3, 6}, {3, 6, 10} and {3, 5, 6, 10}.
%o A357411 (Python)
%o A357411 from fractions import Fraction
%o A357411 from functools import lru_cache
%o A357411 def cond(s, c): h = c/s; return h.denominator == 1 and h.numerator&1
%o A357411 @lru_cache(maxsize=None)
%o A357411 def b(n, s, c):
%o A357411     if n == 0: return int (c > 0 and cond(s, c))
%o A357411     return b(n-1, s, c) + b(n-1, s+Fraction(1, n), c+1)
%o A357411 a = lambda n: b(n, 0, 0)
%o A357411 print([a(n) for n in range(1, 18)]) # _Michael S. Branicky_, Sep 29 2022
%Y A357411 Cf. A339453, A357355, A357412, A357413, A357415.
%K A357411 nonn,more
%O A357411 1,3
%A A357411 _Ilya Gutkovskiy_, Sep 27 2022
%E A357411 a(24)-a(35) from _Michael S. Branicky_, Sep 30 2022