A230093 -id:A230093 - cp's OEIS frontend

A320870 Irregular table: row n >= 0 lists numbers m >= 0 such that n = A062028(m) := m + sum of digits of m.

0, 1, 2, 3, 4, 5, 10, 6, 11, 7, 12, 8, 13, 9, 14, 15, 20, 16, 21, 17, 22, 18, 23, 19, 24, 25, 30, 26, 31, 27, 32, 28, 33, 29, 34, 35, 40, 36, 41, 37, 42, 38, 43, 39, 44, 45, 50, 46, 51, 47, 52, 48, 53, 49, 54, 55, 60, 56, 61, 57, 62, 58, 63, 59, 64, 65, 70, 66, 71, 67, 72, 68, 73, 69, 74, 75, 80, 76, 81, 77, 82, 78, 83, 79, 84, 85, 90

Offset: 0

M. F. Hasler, Nov 09 2018

Row lengths are given by A230093.

			The first nonempty rows are:
    n  | list of m
    0  | 0        // since 0 = 0 + 0
    2  | 1        // since 2 = 1 + 1
    4  | 2        // etc.
    6  | 3        // Below 10 every odd row is empty, but thereafter,
    8  | 4        // only rows 20, 31, 42, ..., 108 (steps of 11),
   10  | 5        // 110, 121, 132, ..., 198, etc. are empty.
   11  | 10       // Since 11 = 10 + (1 + 0)
   12  | 6
   13  | 11       // The first prime that yields a prime: 11 + (1 + 1) = 13.
     (...)
  100  | 86       // The first row of length 2 is 101:
  101  | 91, 100  // 101 = 91 + (9 + 1) = 100 + (1 + 0 + 0)
  102  | 87
     (...)

Robert Israel, Table of n, a(n) for n = 0..9971 (rows 0 to 10000, flattened)

Cf. A007953 (sum of digits of n), A062028 (n + digit sum of n).
Cf. A230093 (number of m such that m + (sum of digits of m) is n).
Cf. A006064 (least m with row length n),
Cf. A003052 (Self or Colombian numbers: rows of length 0), A006378 (Colombian primes).
Cf. A320881 (indices of rows containing a prime), A048520 (primes among these).

N:= 100: # for rows 0 to N, flattened
for i from 0 to N do V[i]:= NULL od:
for i from 0 to N-1 do
  v:= convert(convert(i,base,10),`+`);
  if v <= N then V[v]:= V[v],i fi
od:
seq(V[i],i=1..N); # Robert Israel, Jul 21 2025

A320870_row(n)=if(n,select(m->m+sumdigits(m)==n,[max(n-9*logint(n,10)+8,n\/2)..n-1]),[0])

A358512 a(n) is the smallest number k with exactly n divisors that can be written in the form m + digsum(m), for some m (A176995).

Original entry on oeis.org

1, 2, 4, 8, 12, 30, 24, 80, 48, 72, 96, 192, 120, 180, 288, 612, 240, 624, 420, 360, 480, 900, 1632, 960, 1200, 720, 840, 1560, 2100, 1260, 1440, 3420, 2640, 3024, 1680, 2880, 8316, 4620, 3600, 3780, 4200, 2520, 3360, 6240, 9900, 6300, 7200, 8640, 6720, 13200, 7920

Offset: 0

Marius A. Burtea, Dec 04 2022

			1 cannot be written in the form m + digsum(m), so a(0) = 1.
2 has divisors 1 and 2, and only 2 is written 2 = 1 + digsum(1), so a(1) = 2.
3 has divisors 1 and 3 that cannot be written in the form m + digsum(m).
4 has divisors 1, 2, 4, but only 2 = 1 + digsum(1) and 4 = 2 + digsum(2), so a(2) = 4.

David A. Corneth, Table of n, a(n) for n = 0..2499

Cf. A003052, A062028, A176995, A230093.

f:=func; a:=[]; for n in [0..50] do k:=1; while #[d:d in Divisors(k)|f(d)] ne n do k:=k+1; end while; Append(~a,k); end for; a;

is_A003052(n)={for(i=1, min(n\2, 9*#digits(n)), sumdigits(n-i)==i && return); n}
a(n) = my(k=1); while (sumdiv(k, d, !is_A003052(d)) != n, k++); k; \\ Michel Marcus, Dec 13 2022

A230304 a(n) = 10^( (10^n-1)/9 + n) + 1.

Original entry on oeis.org

101, 10000000000001, 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001

Offset: 1

N. J. A. Sloane, Oct 26 2013

Makowski observes that A230093(a(n)) >= 2 for all n >= 1.

Makowski, Andrzej. On Kaprekar's "junction numbers''. Math. Student 34 1966 77 (1967). MR0223292 (36 #6340)

Index entries for Colombian or self numbers and related sequences

Cf. A006064, A230093, A230094, A230100.

cp's OEIS Frontend

A320870 Irregular table: row n >= 0 lists numbers m >= 0 such that n = A062028(m) := m + sum of digits of m.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

PARI

A358512 a(n) is the smallest number k with exactly n divisors that can be written in the form m + digsum(m), for some m (A176995).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

PARI

A230304 a(n) = 10^( (10^n-1)/9 + n) + 1.

Views

Author

Keywords

Comments

References

Links

Crossrefs