A180157 -id:A180157 - 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

A180160 (sum of digits) mod (number of digits) of n in decimal representation.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 1, 2

Offset: 0

Reinhard Zumkeller, Aug 15 2010

a(n) = A007953(n) mod A055642(n);
a(A061383(n)) = 0; a(A180157(n)) > 0;
a(repdigits)=0: a(A010785(n))=0: a(A002275(n))=0: a(A002276(n))=0: a(A002277(n))=0: a(A002278(n))=0: a(4(n))=0: a(A002279(n))=0: a(A002280(n))=0: a(A002281(n))=0: a(A002282(n))=0: a(A002283(n))=0;
A123522 gives smallest m such that a(m) = n.

Reinhard Zumkeller, Table of n, a(n) for n = 0..25000

Cf. A002275-A002283, A007953, A010785, A055642, A061383, A123522, A180157, A374097.

A180160[n_] := If[n == 0, 0, Mod[Total[#], Length[#]] & [IntegerDigits[n]]];
Array[A180160, 100, 0] (* Paolo Xausa, Jun 30 2024 *)
Join[{0},Table[Mod[Total[IntegerDigits[n]],IntegerLength[n]],{n,110}]] (* Harvey P. Dale, Jul 30 2025 *)

cp's OEIS Frontend

A061383 Arithmetic mean of digits is an integer.

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