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A339663 Number of nonempty subsets of divisors of n whose average is an integer.

%I A339663 #11 Feb 16 2025 08:34:01
%S A339663 1,2,3,4,3,9,3,7,6,6,3,24,3,7,13,12,3,27,3,22,11,7,3,72,6,6,12,21,3,
%T A339663 83,3,20,13,6,11,133,3,7,11,70,3,82,3,21,38,7,3,230,7,14,13,23,3,88,
%U A339663 11,65,11,6,3,763,3,7,35,36,11,84,3,22,13,73,3,780,3,6,37,20,11,82,3,228
%N A339663 Number of nonempty subsets of divisors of n whose average is an integer.
%H A339663 Antti Karttunen, <a href="/A339663/b339663.txt">Table of n, a(n) for n = 1..1079</a>
%H A339663 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ArithmeticMean.html">Arithmetic Mean</a>
%H A339663 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%e A339663 a(16) = 12 subsets: {1}, {2}, {4}, {8}, {16}, {2, 4}, {2, 8}, {2, 16}, {4, 8}, {4, 16}, {8, 16} and {1, 4, 16}.
%o A339663 (PARI)
%o A339663 sumbybits(v,b) = { my(s=0,i=1); while(b>0,s += (b%2)*v[i]; i++; b >>= 1); (s); };
%o A339663 A339663(n) = { my(ds=divisors(n), u=#ds); sum(m=1, (2^u)-1, !(sumbybits(ds,m)%hammingweight(m))); }; \\ _Antti Karttunen_, Dec 12 2021
%Y A339663 Cf. A027750, A051293, A100587, A339664, A339665, A339666.
%K A339663 nonn
%O A339663 1,2
%A A339663 _Ilya Gutkovskiy_, Dec 11 2020