Editing Happy number (section)

===6-happy numbers===
For <math>b = 6</math>, the only positive perfect digital invariant for <math>F_{2, b}</math> is the trivial perfect digital invariant 1, and the only cycle is the eight-number cycle
: 5 → 41 → 25 → 45 → 105 → 42 → 32 → 21 → 5 → ...
and because all numbers are preperiodic points for <math>F_{2, b}</math>, all numbers either lead to 1 and are happy, or lead to the cycle and are unhappy. Because base 6 has no other perfect digital invariants except for 1, no positive integer other than 1 is the sum of the squares of its own digits.

In base 10, the 74 6-happy numbers up to 1296 = 6<sup>4</sup> are (written in base 10):
: 1, 6, 36, 44, 49, 79, 100, 160, 170, 216, 224, 229, 254, 264, 275, 285, 289, 294, 335, 347, 355, 357, 388, 405, 415, 417, 439, 460, 469, 474, 533, 538, 580, 593, 600, 608, 628, 638, 647, 695, 707, 715, 717, 767, 777, 787, 835, 837, 847, 880, 890, 928, 940, 953, 960, 968, 1010, 1018, 1020, 1033, 1058, 1125, 1135, 1137, 1168, 1178, 1187, 1195, 1197, 1207, 1238, 1277, 1292, 1295