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

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

Author

Jaroslav Krizek, Apr 26 2010

Keywords

• nonn

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

• Robert Israel, Table of n, a(n) for n = 1..1009

Crossrefs

Cf. A000203, A004394, A020487, A176797, A327054.

Programs

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

Extensions

More terms from Robert Israel, Sep 05 2024