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

0, 1, 1, 2, 2, 7, 7, 8, 8, 9, 9, 16, 16, 17, 27, 28, 28, 55, 55, 106, 110, 111, 111, 216, 216, 217, 217, 634, 634, 1155, 1155, 1156, 2286, 2287, 3749

Offset: 1

Author

Ilya Gutkovskiy, Sep 27 2022

Keywords

• nonn
• more

Examples

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

Crossrefs

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

Programs

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 == 0
@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)
print([a(n) for n in range(1, 18)]) # Michael S. Branicky, Sep 29 2022

Formula

a(p) = a(p-1) for prime p > 2. - Michael S. Branicky, Sep 30 2022

Extensions

a(24)-a(35) from Michael S. Branicky, Sep 30 2022