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

Author

Ilya Gutkovskiy, Dec 11 2020

Keywords

• nonn

Examples

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

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

Crossrefs

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

Programs

Mathematica

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

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