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%I #12 Dec 30 2018 00:03:40
%S 1,3,1,5,1,1,1,7,5,3,1,2,1,1,1,19,1,3,1,1,1,1,1,3,5,3,1,2,1,1,1,3,1,3,
%T 1,17,1,1,1,7,1,1,1,1,1,1,1,19,1,3,1,5,1,1,1,1,1,3,1,1,1,1,2,13,1,1,1,
%U 1,1,1,1,7,1,3,2,2,1,1,1,19,19,3,1,2,1,1,1,3,1,3,1,1,1,1,1,1,1,3,1,17,1,1,1,7,1
%N a(n) is the smallest natural number m such that product of arithmetic mean of the divisors of n and arithmetic mean of the divisors of m is an integer.
%C a(n) = 1 for infinitely many n.
%C a(n) = 1 for numbers from A003601: a(A003601(n)) = 1.
%C a(n) = 1 iff A057021(n) = 1.
%C Not all terms are 1's or primes. For example, a(128) = 21. - _Antti Karttunen_, Dec 24 2018
%H Antti Karttunen, <a href="/A176801/b176801.txt">Table of n, a(n) for n = 1..16384</a>
%e For n = 12; b(12) = 14/3, a(n) = 2 because b(2) = 3/2; 14/3 * 3/2 = 7 (integer).
%o (PARI) A176801(n) = { my(am=(sigma(n)/numdiv(n))); for(i=1, oo, if(1==denominator(am*(sigma(i)/numdiv(i))), return(i))); }; \\ _Antti Karttunen_, Dec 24 2018
%Y Cf. A000005/A000203 or A057020/A057021: arithmetic mean.
%Y Cf. A003601, A245656.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Apr 26 2010
%E More terms from _Antti Karttunen_, Dec 24 2018
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