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