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

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

Offset

1,3

Links

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

Formula

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

Example

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

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
@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, A357355, A357412, A357413, A357415.

Sequence in context: A051732 A098382 A098180 * A270875 A117752 A299775

Adjacent sequences: A357408 A357409 A357410 * A357412 A357413 A357414

Keyword

nonn,more

Author

Ilya Gutkovskiy, Sep 27 2022

Extensions

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

Status

approved