A052217 -id:A052217 - cp's OEIS frontend

A279771 Numbers n such that the sum of digits of 11n equals 11.

19, 28, 37, 46, 55, 64, 73, 82, 190, 280, 370, 460, 550, 640, 730, 820, 919, 928, 937, 946, 955, 964, 973, 982, 991, 1819, 1828, 1837, 1846, 1855, 1864, 1873, 1882, 1891, 1900, 2728, 2737, 2746, 2755, 2764, 2773, 2782, 2791, 2800, 3637, 3646, 3655, 3664

Offset: 1

M. F. Hasler, Dec 23 2016

Inspired by A088404 = A069537/2 through A088410 = A069543/8.

Cf. A007953 (digital sum), Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).

Select[Range@ 3664, Total@IntegerDigits[11 #] == 11 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI
```
is(n)=sumdigits(11*n)==11
```

A333814 Multiples of 12 whose sum of digits is 12.

Original entry on oeis.org

48, 84, 156, 192, 228, 264, 336, 372, 408, 444, 480, 516, 552, 624, 660, 732, 804, 840, 912, 1056, 1092, 1128, 1164, 1236, 1272, 1308, 1344, 1380, 1416, 1452, 1524, 1560, 1632, 1704, 1740, 1812, 1920, 2028, 2064, 2136, 2172, 2208, 2244, 2280, 2316, 2352, 2424

Offset: 1

Bernard Schott, Apr 06 2020

If m is a term, 10*m is also a term.

			732 = 12 * 61 and 7 + 3 + 2 = 12, hence 732 is a term.

Intersection of A235151 (sum of digits = 12) and A008594 (multiples of 12).
Multiples of k whose sum of digits = k: A011557 (k=1), A069537 (k=2), A052217 (k=3), A063997 (k=4), A069540 (k=5), A062768 (k=6), A063416 (k=7), A069543 (k=8), A052223 (k=9), A333834 (k=10), A283742 (k=11), this sequence (k=12), A283737 (k=13).
Cf. A008594 (multiples of 12), A235151 (sum of digits = 12).
Cf. A057147 (a(n) = n times sum of digits of n).

Select[12 * Range[200], Plus @@ IntegerDigits[#] == 12 &] (* Amiram Eldar, Apr 06 2020 *)

is(n)=sumdigits(n)==12 && n%4==0 \\ Charles R Greathouse IV, Apr 07 2020

a(n) ~ A235151(n). - Charles R Greathouse IV, Apr 07 2020

A333834 Multiples of 10 whose sum of digits is 10.

Original entry on oeis.org

190, 280, 370, 460, 550, 640, 730, 820, 910, 1090, 1180, 1270, 1360, 1450, 1540, 1630, 1720, 1810, 1900, 2080, 2170, 2260, 2350, 2440, 2530, 2620, 2710, 2800, 3070, 3160, 3250, 3340, 3430, 3520, 3610, 3700, 4060, 4150, 4240, 4330, 4420, 4510

Offset: 1

Bernard Schott, Apr 07 2020

If m is a term, 10*m is also a term.

Intersection of A052224 (sum of digits = 10) and A008592 (multiples of 10).

			2440 = 10 * 244 and 2 + 4 + 4 + 0 = 10, hence 2440 is a term.

Multiples of k whose sum of digits = k: A011557 (k=1), A069537 (k=2), A052217 (k=3), A063997 (k=4), A069540 (k=5), A062768 (k=6), A063416 (k=7), A069543 (k=8), A052223 (k=9), this sequence (k=10), A283742 (k=11), A333814 (k=12), A283737 (k=13).
Subsequence of A218292.
Cf. A008592 (multiples of 10), A052224 (sum of digits = 10).
Cf. A057147 (a(n) = n times sum of digits of n)

Select[10 * Range[500], Plus @@ IntegerDigits[#] == 10 &] (* Amiram Eldar, Apr 07 2020 *)

a(n) = 10*A052224(n). - Charles R Greathouse IV, Apr 07 2020

A383971 Triprimes with sum of digits 3.

Original entry on oeis.org

12, 30, 102, 1002, 2001, 10002, 10011, 11001, 20001, 100101, 101001, 110001, 200001, 1000002, 10001001, 10010001, 11000001, 20000001, 100000101, 1000000011, 1000001001, 1000010001, 1000100001, 1001000001, 1010000001, 10000000002, 10000000011, 10000010001, 11000000001, 100000000101, 100000001001

Offset: 1

Robert Israel, May 16 2025

Numbers that are the product of 3 primes, counted with multiplicity, and whose sum of decimal digits is 3.
Since all terms are divisible by 3, the only term ending with 0 is 30. All others are of the form 10^i + 10^j + 1 with 0 <= j <= i.
For each d from 2 to at least 71, there is at least one term with d digits.
Includes 10^k + 2 for k in A076850.
All terms except 12 are squarefree.
All even terms are Zumkeller numbers (A083207). - Ivan N. Ianakiev, May 18 2025

			a(4) = 1002 is a term because 1+0+0+2 = 3 and 1002 = 2 * 3 * 167 is the product of 3 primes, counted with multiplicity.

Robert Israel, Table of n, a(n) for n = 1..380

Intersection of any two of A014612, A050689, and A052217.

Cf. A001222, A007953, A076850, A083207.

istriprime:= proc(n) local F;
  F:= ifactors(n,easy)[2];
  if not hastype(F,symbol) then return convert(F[..,2],`+`)=3 fi;
  F:= remove(hastype,F,symbol);
  if nops(F) > 1 or (nops(F) = 1 and F[1,2] > 1) then return false fi;
  numtheory:-bigomega(n) = 3
end proc:
R:= 12, 30:
for d from 3 to 30 do
  V:= select(istriprime, [seq(seq(10^(d-1) + 10^j + 1,j=0..d-1)]);
  R:= R,op(V);
od:
R;

s={30};imax=11;Do[n=10^i+10^j+1;If[PrimeOmega[n]==3,AppendTo[s,n]],{i,0,imax},{j,0,i}];Sort[s] (* James C. McMahon, Jun 01 2025 *)

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A279771 Numbers n such that the sum of digits of 11n equals 11.

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A333814 Multiples of 12 whose sum of digits is 12.

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A333834 Multiples of 10 whose sum of digits is 10.

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A383971 Triprimes with sum of digits 3.

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