A061425 -id:A061425 - cp's OEIS frontend

A062180 Harmonic mean of digits is 2.

2, 22, 136, 144, 163, 222, 316, 361, 414, 441, 613, 631, 1236, 1244, 1263, 1326, 1333, 1362, 1424, 1442, 1623, 1632, 2136, 2144, 2163, 2222, 2316, 2361, 2414, 2441, 2613, 2631, 3126, 3133, 3162, 3216, 3261, 3313, 3331, 3612, 3621, 4124, 4142, 4214, 4241

Offset: 1

Vladeta Jovovic, Jun 12 2001

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A062179-A062185, A061383-A061388, A061423-A061425.

h:= proc(L) local m,x,i,t;
  m:= nops(L)+1;
  x:= m/2 - add(1/t, t=L);
  if x > 0 then
    x:= 1/x;
    if x::posint and x <= 9 then
      return(x + add(L[i]*10^i,i=1..m-1))
  fi fi
end proc:
f:= n -> h(map(`+`,convert(n,base,9),1)):
g:= n -> h([op(map(`+`,convert(n,base,9),1)),1]):
R:= 2:
for d from 1 to 4 do
  R:= R, seq(f(i),i=9^(d-1)..9^d-1),seq(g(i),i=9^(d-1)..9^d-1)
od:
R; # Robert Israel, Apr 05 2021

Do[ h = IntegerDigits[n]; If[ Sort[h][[1]] != 0 && Length[h]/Apply[Plus, 1/h] == 2, Print[n]], {n, 1, 10^4}]

More terms from Henry Bottomley, Jul 25 2001

A316488 Squares whose arithmetic mean of digits is 8 (i.e., the sum of digits is 8 times the number of digits).

Original entry on oeis.org

97969, 88998998929, 97888999968769, 38999699989995889, 79949788888999969, 98987998979757889, 99497897999899876, 498999778899898896, 597998978979699969, 799778987996998689, 896899597989995889, 899984989899599769, 979978999994798769, 989999999787828969

Offset: 1

Jon E. Schoenfield, Jul 04 2018

Each term's number of digits is in A174438 (Numbers that are congruent to {0, 2, 5, 8} mod 9). For every positive term k in A174438, it appears that this sequence contains at least one k-digit term with the exception of k=2, k=8, and k=9. (See A316480.)

			313^2 = 97969, a 5-digit number whose digit sum is 9+7+9+6+9 = 40 = 8*5, so 97969 is a term.
9949823114^2 = 98998979999888656996, a 20-digit number whose digit sum is 9+8+9+9+8+9+7+9+9+9+9+8+8+8+6+5+6+9+9+6 = 160 = 8*20, so 98998979999888656996 is a term.

Giovanni Resta, Table of n, a(n) for n = 1..97 (terms < 10^28; first 15 terms from Jon E. Schoenfield)

Cf. A069711, A174438, A316480.

Intersection of A000290 and A061425. - Michel Marcus, Jul 06 2018

A062182 Harmonic mean of digits is 4.

Original entry on oeis.org

4, 36, 44, 63, 288, 346, 364, 436, 444, 463, 634, 643, 828, 882, 2488, 2666, 2848, 2884, 3366, 3446, 3464, 3636, 3644, 3663, 4288, 4346, 4364, 4436, 4444, 4463, 4634, 4643, 4828, 4882, 6266, 6336, 6344, 6363, 6434, 6443, 6626, 6633, 6662, 8248, 8284

Offset: 1

Vladeta Jovovic, Jun 12 2001

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A062179-A062185, A061383-A061388, A061423-A061425.

filter:= proc(n) local L;
  L:= convert(n,base,10);
  if has(L,0) then return false fi;
  nops(L)/add(1/i,i=L)=4
end proc:
select(filter, [$1..10^4]); # Robert Israel, Aug 20 2018

Do[ h = IntegerDigits[n]; If[ Sort[h][[1]] != 0 && Length[h]/Apply[Plus, 1/h] == 4, Print[n]], {n, 1, 10^5}]
hm4Q[n_]:=DigitCount[n,10,0]==0&&HarmonicMean[IntegerDigits[n]]==4; Select[Range[9000],hm4Q]  (* Harvey P. Dale, Mar 23 2011 *)

More terms from Henry Bottomley, Jul 25 2001

A062183 Numbers such that harmonic mean of digits is 5.

Original entry on oeis.org

5, 55, 555, 5555, 26999, 28888, 29699, 29969, 29996, 33999, 34688, 34868, 34886, 36488, 36666, 36848, 36884, 38468, 38486, 38648, 38684, 38846, 38864, 39399, 39939, 39993, 43688, 43868, 43886, 44488, 44666, 44848, 44884, 46388, 46466

Offset: 1

Vladeta Jovovic, Jun 12 2001

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

Cf. A062179-A062185, A061383-A061388, A061423-A061425.

Do[ h = IntegerDigits[n]; If[ Sort[h][[1]] != 0 && Length[h]/Apply[Plus, 1/h] == 5, Print[n]], {n, 1, 10^6}]
Select[Range[50000],HarmonicMean[IntegerDigits[#]]==5&] (* Harvey P. Dale, Sep 27 2018 *)

More terms from Robert G. Wilson v, Aug 08 2001

A285093 Corresponding values of arithmetic means of digits of numbers from A061383.

Original entry on oeis.org

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

Offset: 0

Jaroslav Krizek, Apr 14 2017

Jaroslav Krizek, Table of n, a(n) for n = 0..3000

Cf. A061383 (numbers with integer arithmetic mean of digits in base 10).
Sequences of numbers n such that a(n) = k for k = 1 - 9: A061384 (k = 1), A061385 (k = 2), A061386 (k = 3), A061387 (k = 4), A061388 (k = 5), A061423 (k = 6), A061424 (k = 7), A061425 (k = 8), A002283 (k = 9).
Cf. A004426, A004427, A257295 (supersequences).

[0] cat [&+Intseq(n) / #Intseq(n): n in [1..100000] | &+Intseq(n) mod #Intseq(n) eq 0];

lista(nn) = {for (n=0, nn, if (n, d = digits(n), d = [0]); if (!( vecsum(d) % #d), print1(vecsum(d)/#d, ", ")););} \\ Michel Marcus, Apr 15 2017

a(n) = A007953(A061383(n)) / A055642(A061383(n)) for n >= 1.

A061546 Harmonic mean of digits is 7.

Original entry on oeis.org

7, 77, 777, 7777, 77777, 777777, 3999999, 4688999, 4689899, 4689989, 4689998, 4698899, 4698989, 4698998, 4699889, 4699898, 4699988, 4868999, 4869899, 4869989, 4869998, 4886999, 4888888, 4889699, 4889969, 4889996, 4896899

Offset: 1

Vladeta Jovovic, Jun 13 2001

			6666999 is a term since 7/(1/6+1/6+1/6+1/6+1/9+1/9+1/9)=7.

Cf. A062179-A062185, A061383-A061388, A061423-A061425.

Do[ h = IntegerDigits[n]; If[ Sort[h][[1]] != 0 && Length[h]/Apply[Plus, 1/h] == 7, Print[n]], {n, 1, 10^6}]

More terms from Robert G. Wilson v, Aug 08 2001

A062181 Harmonic mean of digits is 3.

Original entry on oeis.org

3, 26, 33, 62, 236, 244, 263, 326, 333, 362, 424, 442, 623, 632, 1999, 2266, 2336, 2344, 2363, 2434, 2443, 2626, 2633, 2662, 3236, 3244, 3263, 3326, 3333, 3362, 3424, 3442, 3623, 3632, 4234, 4243, 4324, 4342, 4423, 4432, 6226, 6233, 6262, 6323, 6332

Offset: 1

Vladeta Jovovic, Jun 12 2001

Eric Weisstein's World of Mathematics, Harmonic Mean.
Wikipedia, Harmonic mean.

Cf. A062179-A062185, A061383-A061388, A061423-A061425.

Do[ h = IntegerDigits[n]; If[ Sort[h][[1]] != 0 && Length[h]/Apply[Plus, 1/h] == 3, Print[n]], {n, 1, 10^4}]

from fractions import Fraction
def hm(n):
  s = str(n)
  return None if '0' in s else len(s)/sum(Fraction(1, int(d)) for d in s)
def aupto(limit): return [m for m in range(limit+1) if hm(m) == 3]
print(aupto(6332)) # Michael S. Branicky, Mar 26 2021

More terms from Henry Bottomley, Jul 25 2001

A062184 Harmonic mean of digits is 6.

Original entry on oeis.org

6, 66, 488, 666, 848, 884, 3999, 4688, 4868, 4886, 6488, 6666, 6848, 6884, 8468, 8486, 8648, 8684, 8846, 8864, 9399, 9939, 9993, 36999, 38888, 39699, 39969, 39996, 44999, 46688, 46868, 46886, 48668, 48686, 48866, 49499, 49949, 49994, 63999

Offset: 1

Vladeta Jovovic, Jun 12 2001

Cf. A062179-A062185, A061383-A061388, A061423-A061425.

Do[ h = IntegerDigits[n]; If[ Sort[h][[1]] != 0 && Length[h]/Apply[Plus, 1/h] == 6, Print[n]], {n, 1, 10^6}]

More terms from Robert G. Wilson v, Aug 08 2001

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A062180 Harmonic mean of digits is 2.

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A316488 Squares whose arithmetic mean of digits is 8 (i.e., the sum of digits is 8 times the number of digits).

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A062182 Harmonic mean of digits is 4.

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A062183 Numbers such that harmonic mean of digits is 5.

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A285093 Corresponding values of arithmetic means of digits of numbers from A061383.

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A061546 Harmonic mean of digits is 7.

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A062181 Harmonic mean of digits is 3.

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A062184 Harmonic mean of digits is 6.

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