A175688 -id:A175688 - cp's OEIS frontend

A061383 Arithmetic mean of digits is an integer.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 19, 20, 22, 24, 26, 28, 31, 33, 35, 37, 39, 40, 42, 44, 46, 48, 51, 53, 55, 57, 59, 60, 62, 64, 66, 68, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 91, 93, 95, 97, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129

Offset: 0

Amarnath Murthy, May 03 2001

A004426(a(n)) = A004427(a(n)). - Reinhard Zumkeller, May 27 2010
A175688 is a subsequence; complement of A180157; A180160(a(n))=0. - Reinhard Zumkeller, Aug 15 2010
It seems "obvious" that n log n << a(n) < n log n; is this true? - Charles R Greathouse IV, Feb 06 2013

			123 is a term as the arithmetic mean is (1+2+3)/3 = 2.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A007953, A055642.
Cf. A004426, A004427.
Cf. A175688, A180157, A180160.

a061383 n = a061383_list !! (n-1)
a061383_list = filter (\x -> mod (a007953 x) (a055642 x) == 0) [0..]
-- Reinhard Zumkeller, Jun 18 2013

[0] cat [n: n in [1..130] | IsZero(&+Intseq(n) mod #Intseq(n))];  // Bruno Berselli, Jun 30 2011

[0] cat [n: n in [1..130] | IsIntegral(&+Intseq(n)/#Intseq(n))];   // Bruno Berselli, Feb 09 2016

Select[Range[0,129],IntegerQ[Total[x=IntegerDigits[#]]/Length[x]] &] (* Jayanta Basu, May 17 2013 *)
Select[Range[0,200],IntegerQ[Mean[IntegerDigits[#]]]&] (* Harvey P. Dale, Dec 31 2022 *)

is(n)=my(v=digits(n));sum(i=1,#v,v[i])%#v==0 \\ Charles R Greathouse IV, Feb 06 2013

def ok(n): return n == 0 or sum(d:=list(map(int, str(n))))%len(d) == 0
print([k for k in range(130) if ok(k)]) # Michael S. Branicky, Apr 23 2025

A052018 Numbers k with the property that the sum of the digits of k is a substring of k.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 200, 300, 400, 500, 600, 700, 800, 900, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 1000, 1009, 1018, 1027, 1036, 1045, 1054, 1063

Offset: 1

Patrick De Geest, Nov 15 1999

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A052019, A052020, A052021, A052022, A007953, A005349, A028834.
Cf. A175688. - Reinhard Zumkeller, Aug 15 2010
Cf. A055642, A004426.
Cf. A119246, A138166.

import Data.List (isInfixOf)
a052018 n = a052018_list !! (n-1)
a052018_list = filter f [0..] where
   f x = show (a007953 x) `isInfixOf` show x
-- Reinhard Zumkeller, Jun 18 2013

sdssQ[n_]:=Module[{idn=IntegerDigits[n],s,len},s=Total[idn];len= IntegerLength[ s]; MemberQ[Partition[idn,len,1],IntegerDigits[s]]]; Join[{0},Select[Range[1100],sdssQ]] (* Harvey P. Dale, Jan 02 2013 *)

loop = (str(n) for n in range(399))
print([int(n) for n in loop if str(sum(int(k) for k in n)) in n]) # Jonathan Frech, Jun 05 2017

A004426 Arithmetic mean of digits of n (rounded down).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 0, 0, 1, 1, 1, 2, 2, 2

Offset: 0

N. J. A. Sloane

From Reinhard Zumkeller, May 27 2010: (Start)
A004427(n) <= a(n);
a(A061383(n)) = A004427(A061383(n));
a(A000040(n)) = A074461(n). (End)

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for Colombian or self numbers and related sequences

Cf. A175688.

a004426 n = (a007953 n) `div` (a055642 n)
-- Reinhard Zumkeller, Jun 18 2013

Table[Floor[Mean[IntegerDigits[n]]], {n, 0, 99}] (* Enrique Pérez Herrero, Sep 28 2013 *)

a(n) = floor(A007953(n)/A055642(n)). - Reinhard Zumkeller, May 27 2010

A378560 Numbers with the median of the digits equal to one of the digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140

Offset: 1

Stefano Spezia, Nov 30 2024

			10 is not in the list because the median of its digits is not integer.
13 is not in the list because the median of its digits is 2 which is not a digit of 13.
113 is in the list because the median of its digits is 1 which is a digit of 113.

Stefano Spezia, Table of n, a(n) for n = 1..10000

Cf. A001633 (subsequence), A175688, A378564.

Cf. A292730, A292739, A366207, A366208, A366209, A366210, A366211, A366212, A366213, A366214.

Select[Range[0,140],MemberQ[digits=IntegerDigits[#],Median[digits]] &]

A175758 Numbers n with property that arithmetic mean of its digits is both an integer and one of the prime factors of n.

Original entry on oeis.org

2, 3, 5, 7, 15, 22, 24, 33, 40, 42, 51, 55, 60, 77, 108, 114, 117, 126, 132, 135, 144, 150, 153, 162, 171, 180, 195, 204, 207, 216, 222, 225, 234, 240, 243, 252, 261, 270, 285, 306, 312, 315, 324, 330, 333, 342, 351, 360, 375, 399, 402, 405, 414, 420, 423, 432

Offset: 1

Juri-Stepan Gerasimov, Aug 28 2010, Aug 29 2010

			15 is in the list because (1+5)/2=3 and 3 is a prime factor of 15.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A027746, A175688.

ipfQ[n_]:=Module[{m=Mean[IntegerDigits[n]]},IntegerQ[m]&&MemberQ[ FactorInteger[ n][[All,1]],m]]; Select[Range[2,500],ipfQ] (* Harvey P. Dale, Feb 15 2020 *)

399 inserted by D. S. McNeil, Sep 27 2010

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A061383 Arithmetic mean of digits is an integer.

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A052018 Numbers k with the property that the sum of the digits of k is a substring of k.

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A004426 Arithmetic mean of digits of n (rounded down).

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A378560 Numbers with the median of the digits equal to one of the digits.

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A175758 Numbers n with property that arithmetic mean of its digits is both an integer and one of the prime factors of n.

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