A339665 Number of nonempty subsets of divisors of n whose harmonic mean is an integer.

1, 2, 2, 3, 2, 9, 2, 4, 3, 4, 2, 17, 2, 4, 6, 5, 2, 19, 2, 10, 4, 4, 2, 37, 3, 4, 4, 12, 2, 45, 2, 6, 4, 4, 4, 57, 2, 4, 4, 28, 2, 29, 2, 6, 16, 4, 2, 85, 3, 6, 4, 6, 2, 35, 4, 23, 4, 4, 2, 301, 2, 4, 6, 7, 4, 28, 2, 6, 4, 19, 2, 255, 2, 4, 10, 6, 4, 20, 2, 61

Offset

1,2

Links

Chai Wah Wu, Table of n, a(n) for n = 1..3000

Eric Weisstein's World of Mathematics, Harmonic Mean

Index entries for sequences related to divisors of numbers

Example

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

Mathematica

a[n_] := Count[Subsets[Divisors[n]], _?(Length[#] > 0 && IntegerQ[HarmonicMean[#]] &)]; Array[a, 100] (* Amiram Eldar, Nov 09 2021 *)

Prog

(PARI) h(s, d) = #s/sum(k=1, #s, 1/d[s[k]]);
a(n) = my(d=divisors(n), nb=0); forsubset(#d, s, if (#s && (denominator(h(s, d))==1), nb++)); nb; \\ Michel Marcus, Dec 15 2020
(Python)
from itertools import combinations
from sympy import divisors
def A339665(n):
    ds = tuple(divisors(n, generator=True))
    return sum(sum(1 for d in combinations(ds, i) if n*i % sum(d) == 0) for i in range(1, len(ds)+1)) # Chai Wah Wu, Nov 09 2021

Crossrefs

Cf. A027750, A100587, A339453, A339663, A339664, A339666.

Sequence in context: A369748 A280583 A177047 * A334490 A016001 A016012

Adjacent sequences: A339662 A339663 A339664 * A339666 A339667 A339668

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 11 2020

Status

approved