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A327054 a(n) is the smallest number m such that the antiharmonic mean of the divisors is n, or 0 if no such m exists. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
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.
LINKS
EXAMPLE
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.
PROG
(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]]
CROSSREFS
Sequence in context: A352729 A286875 A105570 * A101419 A060278 A046770
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Oct 06 2019
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)