In standard notation, there are two ways to represent 2: 10, in base 2, and 2 in every other base. Accordingly, there are three ways to represent 3: 11 in base 2, 10 in base 3, and 3 in every other base. There are four ways to represent 4, five ways to represent 5, and so on. Now, suppose you sum all the digits of all the representations of n in the bases 2 to n, like this:

Σ(2) = 1+0₂ = 1
Σ(3) = 1+1₂ + 1+0₃ = 3 (+2)
Σ(4) = 1+0+0₂ + 1+1₃ + 1+0₄ = 4 (+1)
Σ(5) = 1+0+1₂ + 1+2₃ + 1+1₄ + 1+0₅ = 8 (+4)
Σ(6) = 1+1+0₂ + 2+0₃ + 1+2₄ + 1+1₅ + 1+0₆ = 10 (+2)
Σ(7) = 1+1+1₂ + 2+1₃ + 1+3₄ + 1+2₅ + 1+1₆ + 1+0₇ = 16 (+6)
Σ(8) = 1+0+0+0₂ + 2+2₃ + 2+0₄ + 1+3₅ + 1+2₆ + 1+1₇ + 1+0₈ = 17 (+1)
Σ(9) = 1+0+0+1₂ + 1+0+0₃ + 2+1₄ + 1+4₅ + 1+3₆ + 1+2₇ + 1+1₈ + 1+0₉ = 21 (+4)
Σ(10) = 1+0+1+0₂ + 1+0+1₃ + 2+2₄ + 2+0₅ + 1+4₆ + 1+3₇ + 1+2₈ + 1+1₉ + 1+0₁₀ = 25 (+4)

It seems reasonable to suppose that as n increases, so the all-digit-sum of n increases. But that isn’t always the case: occasionally it decreases. Here are the sums for n=11..100 (with prime factors when the sum is composite):

Σ(11) = 35 = 5·7 (+10)
Σ(12) = 34 = 2·17 (-1)
Σ(13) = 46 = 2·23 (+12)
Σ(14) = 52 = 2²·13 (+6)
Σ(15) = 60 = 2²·3·5 (+8)
Σ(16) = 58 = 2·29 (-2)
Σ(17) = 74 = 2·37 (+16)
Σ(18) = 73 (-1)
Σ(19) = 91 = 7·13 (+18)
Σ(20) = 92 = 2²·23 (+1)
Σ(21) = 104 = 2³·13 (+12)
Σ(22) = 114 = 2·3·19 (+10)
Σ(23) = 136 = 2³·17 (+22)
Σ(24) = 128 = 2⁷ (-8)
Σ(25) = 144 = 2⁴·3² (+16)
Σ(26) = 156 = 2²·3·13 (+12)
Σ(27) = 168 = 2³·3·7 (+12)
Σ(28) = 171 = 3²·19 (+3)
Σ(29) = 199 (+28)
Σ(30) = 193 (-6)
Σ(31) = 223 (+30)
Σ(32) = 221 = 13·17 (-2)
Σ(33) = 241 (+20)
Σ(34) = 257 (+16)
Σ(35) = 281 (+24)
Σ(36) = 261 = 3²·29 (-20)
Σ(37) = 297 = 3³·11 (+36)
Σ(38) = 315 = 3²·5·7 (+18)
Σ(39) = 339 = 3·113 (+24)
Σ(40) = 333 = 3²·37 (-6)
Σ(41) = 373 (+40)
Σ(42) = 367 (-6)
Σ(43) = 409 (+42)
Σ(44) = 416 = 2⁵·13 (+7)
Σ(45) = 430 = 2·5·43 (+14)
Σ(46) = 452 = 2²·113 (+22)
Σ(47) = 498 = 2·3·83 (+46)
Σ(48) = 472 = 2³·59 (-26)
Σ(49) = 508 = 2²·127 (+36)
Σ(50) = 515 = 5·103 (+7)
Σ(51) = 547 (+32)
Σ(52) = 556 = 2²·139 (+9)
Σ(53) = 608 = 2⁵·19 (+52)
Σ(54) = 598 = 2·13·23 (-10)
Σ(55) = 638 = 2·11·29 (+40)
Σ(56) = 634 = 2·317 (-4)
Σ(57) = 670 = 2·5·67 (+36)
Σ(58) = 698 = 2·349 (+28)
Σ(59) = 756 = 2²·3³·7 (+58)
Σ(60) = 717 = 3·239 (-39)
Σ(61) = 777 = 3·7·37 (+60)
Σ(62) = 807 = 3·269 (+30)
Σ(63) = 831 = 3·277 (+24)
Σ(64) = 819 = 3²·7·13 (-12)
Σ(65) = 867 = 3·17² (+48)
Σ(66) = 861 = 3·7·41 (-6)
Σ(67) = 927 = 3²·103 (+66)
Σ(68) = 940 = 2²·5·47 (+13)
Σ(69) = 984 = 2³·3·41 (+44)
Σ(70) = 986 = 2·17·29 (+2)
Σ(71) = 1056 = 2⁵·3·11 (+70)
Σ(72) = 1006 = 2·503 (-50)
Σ(73) = 1078 = 2·7²·11 (+72)
Σ(74) = 1114 = 2·557 (+36)
Σ(75) = 1140 = 2²·3·5·19 (+26)
Σ(76) = 1155 = 3·5·7·11 (+15)
Σ(77) = 1215 = 3⁵·5 (+60)
Σ(78) = 1209 = 3·13·31 (-6)
Σ(79) = 1287 = 3²·11·13 (+78)
Σ(80) = 1263 = 3·421 (-24)
Σ(81) = 1293 = 3·431 (+30)
Σ(82) = 1333 = 31·43 (+40)
Σ(83) = 1415 = 5·283 (+82)
Σ(84) = 1368 = 2³·3²·19 (-47)
Σ(85) = 1432 = 2³·179 (+64)
Σ(86) = 1474 = 2·11·67 (+42)
Σ(87) = 1530 = 2·3²·5·17 (+56)
Σ(88) = 1530 = 2·3²·5·17 (=)
Σ(89) = 1618 = 2·809 (+88)
Σ(90) = 1572 = 2²·3·131 (-46)
Σ(91) = 1644 = 2²·3·137 (+72)
Σ(92) = 1663 (+19)
Σ(93) = 1723 (+60)
Σ(94) = 1769 = 29·61 (+46)
Σ(95) = 1841 = 7·263 (+72)
Σ(96) = 1784 = 2³·223 (-57)
Σ(97) = 1880 = 2³·5·47 (+96)
Σ(98) = 1903 = 11·173 (+23)
Σ(99) = 1947 = 3·11·59 (+44)
Σ(100) = 1923 = 3·641 (-24)

The sum usually increases, occasionally decreases. In one case, when 87 = n = 88, it stays the same. This also happens when 463 = n = 464, where Σ(463) = Σ(464) = 39,375. Does it happen again? I don’t know. The ratio of sum-ups to sum-downs seems to tend towards 3:1. Is that the exact ratio at infinity? I don’t know. Watch this sbase.