login
A176799
a(n) = possible values of A176797(m) in increasing order, where A176797(m) = antiharmonic means of divisors of antiharmonic numbers A020487.
2
1, 3, 7, 11, 13, 21, 35, 43, 61, 63, 77, 85, 91, 111, 119, 129, 147, 157, 171, 183, 185, 231, 245, 255, 273, 301, 313, 333, 343, 425, 441, 455, 471, 473, 481, 507, 521, 547, 559, 629, 671, 683, 741, 765, 777, 793, 813, 819, 833, 841, 845, 903, 931, 935, 1015, 1029, 1099, 1105, 1183, 1197, 1221
OFFSET
1,2
COMMENTS
From Robert Israel, Sep 05 2024: (Start)
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).
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)
LINKS
MAPLE
# This uses the b-file for A004394
K:= 10000: # 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:
select(v -> V[v] > 0, [$1..K]); # Robert Israel, Sep 05 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Apr 26 2010
EXTENSIONS
More terms from Robert Israel, Sep 05 2024
STATUS
approved