|
|
A353543
|
|
Primitive terms of A353537.
|
|
2
|
|
|
4, 6, 10, 14, 45, 63, 75, 105, 165, 195, 231, 242, 255, 285, 286, 345, 374, 418, 435, 442, 465, 494, 506, 598, 638, 646, 682, 754, 782, 806, 814, 874, 902, 946, 962, 1034, 1066, 1118, 1166, 1222, 1287, 1298, 1342, 1378, 1474, 1562, 1606, 1683, 1738, 1826, 1881
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
If a number is in A353537 then all its multiples are in it. Therefore, the terms of A353537 whose proper divisors are not in A353537 are the primitive terms.
|
|
LINKS
|
|
|
EXAMPLE
|
4 is a term since sigma(4)/4 = 7/4 = 1.75 > Pi^2/6 = 1.644..., the proper divisors of 4 are 1 and 2, sigma(1)/1 = 1 < Pi^2/6 and sigma(2)/2 = 3/2 < Pi^2/6.
|
|
MATHEMATICA
|
q[n_] := DivisorSigma[-1, n] > Pi^2/6 && AllTrue[Most @ Divisors[n], DivisorSigma[-1, #] < Pi^2/6 &]; Select[Range[2000], q]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|