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A043000 Number of digits in all base b representations of n, for 2 <= b <= n. 4
2, 4, 7, 9, 11, 13, 16, 19, 21, 23, 25, 27, 29, 31, 35, 37, 39, 41, 43, 45, 47, 49, 51, 54, 56, 59, 61, 63, 65, 67, 70, 72, 74, 76, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..59.

FORMULA

a(n) = Sum_{i=2..n} floor(log_i(i*n)); a(n) = n*log_2(n) + O(n). - Vladimir Shevelev, Jun 03 2011

a(n) = A070939(n) + A081604(n) + A110591(n) + ... + 1. - R. J. Mathar, Jun 04 2011

From Ridouane Oudra, Nov 13 2019: (Start)

a(n) = Sum_{i=1..n-1} floor(n^(1/i));

a(n) = n - 1 + Sum_{i=1..floor(log_2(n))} floor(n^(1/i) - 1);

a(n) = n - 1 + A255165(n). (End)

EXAMPLE

5 = 101_2 = 12_3 = 11_4 = 10_5. Thus a(5) = 3+2+2+2 = 9.

MAPLE

A043000 := proc(n) add( nops(convert(n, base, b)), b=2..n) ; end proc: # R. J. Mathar, Jun 04 2011

MATHEMATICA

Table[Total[IntegerLength[n, Range[2, n]]], {n, 2, 60}] (* Harvey P. Dale, Apr 23 2019 *)

PROG

(MAGMA) [&+[Floor(Log(i, i*n)):k in [2..n]]:n in [1..70]]; // Marius A. Burtea, Nov 13 2019

CROSSREFS

Cf. A043306, A068953, A191322, A255165.

Sequence in context: A287723 A284589 A020904 * A160822 A111495 A187686

Adjacent sequences:  A042997 A042998 A042999 * A043001 A043002 A043003

KEYWORD

nonn,base,changed

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)