A176799 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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

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

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);