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, 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

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

Robert Israel, Table of n, a(n) for n = 1..10000

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.

Maple

# This uses the b-file for A004394
# See comment at A176799
K:= 100: # to get terms <= K
M:= 36 * K^2/Pi^4:
for i from 1 while A004394[i] < M do od:
r:= numtheory:-sigma(A004394[i])/A004394[i]:
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:
convert(V, list); # Robert Israel, Sep 05 2024

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

Cf. A020487, A176797, A176799, A176800.

Cf. A000290, A004394, A091911, A162538.

Sequence in context: A352729 A286875 A105570 * A101419 A060278 A046770

Adjacent sequences: A327051 A327052 A327053 * A327055 A327056 A327057

Keyword

nonn

Author

Jaroslav Krizek, Oct 06 2019

Status

approved