cp's OEIS Frontend

A176799 a(n) = possible values of A176797(m) in increasing order, where A176797(m) = antiharmonic means of divisors of antiharmonic numbers A020487.

%I A176799 #11 Sep 06 2024 20:15:42
%S A176799 1,3,7,11,13,21,35,43,61,63,77,85,91,111,119,129,147,157,171,183,185,
%T A176799 231,245,255,273,301,313,333,343,425,441,455,471,473,481,507,521,547,
%U A176799 559,629,671,683,741,765,777,793,813,819,833,841,845,903,931,935,1015,1029,1099,1105,1183,1197,1221
%N A176799 a(n) = possible values of A176797(m) in increasing order, where A176797(m) = antiharmonic means of divisors of antiharmonic numbers A020487.
%C A176799 From _Robert Israel_, Sep 05 2024: (Start)
%C A176799 According to A000203, sigma_1(m) <= (6/Pi^2)*m^(3/2) for m >= 12. Thus since sigma_2(m) > m^2, sigma_2(m)/sigma_1(m) > (Pi^2/6) * m^(1/2).
%C A176799 This would suggest that to find all terms <= K of this sequence we should look at sigma_2(m)/sigma_1(m) for m <= 36 * K^2/Pi^4.  But using the b-file for A004394 we may get a good upper bound for sigma_1(m)/m for m in this interval, resulting in a much smaller search region. (End)
%H A176799 Robert Israel, <a href="/A176799/b176799.txt">Table of n, a(n) for n = 1..1009</a>
%p A176799 # This uses the b-file for A004394
%p A176799 K:= 10000: # to get terms <= K
%p A176799 M:= 36 * K^2/Pi^4:
%p A176799 for i from 1 while A004394[i] < M do od:
%p A176799 r:= numtheory:-sigma(A004394[i])/A004394[i]:
%p A176799 V:= Vector(K):
%p A176799 for m from 1 to r*K do
%p A176799   F:= numtheory:-divisors(m);
%p A176799 v:= add(d^2, d=F)/add(d,d=F);
%p A176799 if v::integer and v <= K and V[v] = 0 then V[v]:= m fi;
%p A176799 od:
%p A176799 select(v -> V[v] > 0, [$1..K]); # _Robert Israel_, Sep 05 2024
%Y A176799 Cf. A000203, A004394, A020487, A176797, A327054.
%K A176799 nonn
%O A176799 1,2
%A A176799 _Jaroslav Krizek_, Apr 26 2010
%E A176799 More terms from _Robert Israel_, Sep 05 2024