A327054 - OEIS

%I #24 Sep 20 2024 11:06:18

%S 1,0,4,0,0,0,9,0,0,0,16,0,20,0,0,0,0,0,0,0,25,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,50,0,0,0,0,0,0,0,49,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,81,0,100,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,144,0,0,0,0,0,0,0

%N a(n) is the smallest number m such that the antiharmonic mean of the divisors is n, or 0 if no such m exists.

%C a(n) = the smallest number m such that sigma_2(n) / sigma_1(n) = A001157(m) / A000203(m) = n, or 0 if no such m exists.

%C Zeros occur if n is not in A176799.

%C See A000290, A091911 and A162538 for like sequences for geometric, arithmetic and harmonic means of the divisors.

%H Robert Israel, <a href="/A327054/b327054.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 4 because 4 is the smallest number m with sigma_2(m) / sigma_1(m) = 3; sigma_2(4) / sigma_1(4) = 21 / 7 = 3.

%p # This uses the b-file for A004394

%p # See comment at A176799

%p K:= 100: # to get terms <= K

%p M:= 36 * K^2/Pi^4:

%p for i from 1 while A004394[i] < M do od:

%p r:= numtheory:-sigma(A004394[i])/A004394[i]:

%p V:= Vector(K):

%p for m from 1 to r*K do

%p   F:= numtheory:-divisors(m);

%p   v:= add(d^2, d=F)/add(d, d=F);

%p   if v::integer and v <= K and V[v] = 0 then V[v]:= m fi;

%p od:

%p convert(V,list); # _Robert Israel_, Sep 05 2024

%o (Magma) A327054:=func<n|exists(r){m:m in[1..10000] |  IsIntegral(&+[d^2: d in Divisors(m)] / SumOfDivisors(m)) and (&+[d^2: d in Divisors(m)] / SumOfDivisors(m)) eq n}select r else 0>; [A327054(n): n in[1..100]];

%Y Cf. A020487, A176797, A176799, A176800.

%Y Cf. A000290, A004394, A091911, A162538.

%K nonn

%O 1,3

%A _Jaroslav Krizek_, Oct 06 2019