A357411 - OEIS

%I #25 Sep 30 2022 14:37:07

%S 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 165,166,458,459,865,866,866,1647,1669,2724

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

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

%e a(11) = 10 subsets: {1}, {3}, {5}, {7}, {9}, {11}, {2, 6}, {2, 3, 6}, {3, 6, 10} and {3, 5, 6, 10}.

%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

%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, A357355, A357412, A357413, A357415.

%K nonn,more

%O 1,3

%A _Ilya Gutkovskiy_, Sep 27 2022

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