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A327054
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a(n) is the smallest number m such that the antiharmonic mean of the divisors is n, or 0 if no such m exists.
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2
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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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,3
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COMMENTS
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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.
Zeros occur if n is not in A176799.
See A000290, A091911 and A162538 for like sequences for geometric, arithmetic and harmonic means of the divisors.
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LINKS
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EXAMPLE
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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.
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MAPLE
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K:= 100: # to get terms <= K
M:= 36 * K^2/Pi^4:
for i from 1 while A004394[i] < M do od:
V:= Vector(K):
for m from 1 to r*K do
F:= numtheory:-divisors(m);
v:= add(d^2, d=F)/add(d, d=F);
if v::integer and v <= K and V[v] = 0 then V[v]:= m fi;
od:
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PROG
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(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]]
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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