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

1,4

Links

Table of n, a(n) for n=1..35.

Formula

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A261710 A064288 A054085 * A021443 A045923 A306238

Adjacent sequences: A357409 A357410 A357411 * A357413 A357414 A357415

Keyword

nonn,more

Author

Ilya Gutkovskiy, Sep 27 2022

Extensions

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

Status

approved