A066564 -id:A066564 - cp's OEIS frontend

A062028 a(n) = n + sum of the digits of n.

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

Offset: 0

Amarnath Murthy, Jun 02 2001

a(n) = A248110(n,A007953(n)). - Reinhard Zumkeller, Oct 01 2014

			a(34) = 34 + 3 + 4 = 41, a(40) = 40 + 4 = 44.

Harry J. Smith and N. J. A. Sloane, Table of n, a(n) for n = 0..10000 (first 1000 terms were computed by Harry J. Smith)
Index entries for Colombian or self numbers and related sequences

Cf. A007953, A006378, A048521, A107740, A066568, A064806, A176995 (range), A003052, A230093, A248110.
Indices of: A047791 (primes), A107743 (composites), A066564 (squares), A084661 (cubes).
Iterations: A004207 (start=1), A016052 (start=3), A007618 (start=5), A006507 (start=7), A016096 (start=9).

a062028 n = a007953 n + n  -- Reinhard Zumkeller, Oct 11 2013

with(numtheory): for n from 1 to 100 do a := convert(n,base,10):
c := add(a[i],i=1..nops(a)): printf(`%d,`,n+c); od:
A062028 := n -> n+add(i,i=convert(n,base,10)) # M. F. Hasler, Nov 08 2018

Table[n + Total[IntegerDigits[n]], {n, 0, 100}]

A062028(n)=n+sumdigits(n) \\ M. F. Hasler, Jul 19 2015

def a(n): return n + sum(map(int, str(n)))
print([a(n) for n in range(71)]) # Michael S. Branicky, Jan 09 2023

a(n) = n + A007953(n).

a(n) = A160939(n+1) - 1. - Filip Zaludek, Oct 26 2016

More terms from Vladeta Jovovic, Jun 05 2001

A066566 Numbers that when decremented by the sum of their digits produce a square.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 330, 331, 332, 333

Offset: 1

Amarnath Murthy, Dec 18 2001

The squares in this sequence are divisible by 9.

			155 is a member as 155 - 1 - 5 - 5 = 144 = 12^2.

Indranil Ghosh, Table of n, a(n) for n = 1..11130 (terms 1..1000 from Harry J. Smith)

Cf. A066564.

Select[Range[0,350],IntegerQ[Sqrt[#-Total[IntegerDigits[#]]]]&]  (* Harvey P. Dale, Feb 24 2011 *)

PARI
```
isok(k)={issquare(k-sumdigits(k))}
```

More terms from Jason Earls, Dec 20 2001

Offset changed from 0 to 1 by Harry J. Smith, Mar 05 2010

A066567 Numbers that when incremented by the product of their digits produce a square.

Original entry on oeis.org

2, 8, 13, 63, 91, 100, 128, 185, 215, 221, 337, 400, 448, 456, 549, 551, 559, 681, 900, 1024, 1089, 1151, 1185, 1215, 1221, 1327, 1348, 1437, 1600, 1651, 1897, 2025, 2112, 2191, 2196, 2209, 2293, 2304, 2392, 2401, 2448, 2500, 2539, 2544, 2551, 2596, 2601

Offset: 1

Amarnath Murthy, Dec 18 2001

			63 belongs to this sequence as 63 + 6*3 = 81 = 9^2.

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A000290, A066564, A230099.

f[n_] := n + Apply[ Times, IntegerDigits[n]]; Select[ Range[ 2500], IntegerQ[ Sqrt[ f[ # ]]] & ]
Select[Range[3000],IntegerQ[Sqrt[#+Times@@IntegerDigits[#]]]&] (* Harvey P. Dale, Sep 15 2024 *)

isok(k) = issquare(k+vecprod(digits(k))); \\ Harry J. Smith, Mar 05 2010

More terms from Robert G. Wilson v, Dec 22 2001

Offset changed from 0 to 1 by Harry J. Smith, Mar 05 2010

A084661 Numbers k such that k + sum_of_digits(k) is a cube.

Original entry on oeis.org

4, 18, 121, 198, 207, 329, 720, 977, 1318, 2183, 2731, 3357, 4082, 4891, 4900, 5814, 6836, 7969, 9243, 10634, 12154, 13797, 13806, 15611, 17554, 19656, 21929, 24367, 26973, 29759, 32746, 39281, 42853, 46629, 54850, 59292, 59301, 63968, 68890, 74070, 79475

Offset: 1

Zak Seidov, Jun 29 2003

A066564 lists numbers k such that k + sum_of_digits(k) is a square.

			a(3)=121 because 121 + (1 + 2 + 1) = 125 = 5^3.

Harvey P. Dale, Table of n, a(n) for n = 1..250

Cf. A062028, A066564.

Select[Range[80000],IntegerQ[Surd[#+Total[IntegerDigits[#]],3]]&] (* Harvey P. Dale, Sep 13 2018 *)

isok(n) = ispower(n + sumdigits(n), 3); \\ Michel Marcus, Oct 09 2013

More terms from Michel Marcus, Oct 04 2013

A230087 Primes such that prime plus its digit sum is a perfect square.

Original entry on oeis.org

2, 17, 179, 347, 467, 521, 1433, 1583, 2111, 3347, 10601, 12527, 25889, 28541, 32027, 33113, 39569, 39971, 41201, 43661, 45767, 55667, 58061, 59513, 61001, 62969, 63977, 67061, 70199, 77261, 92387, 92993, 100469, 109541, 120401, 122477, 130307, 156011, 163193

Offset: 1

K. D. Bajpai, Oct 08 2013

Number of primes obtained from the sequence ‘prime plus its digit sum is perfect square’ is 150 for n = 1 to 3*10^5, while the sequence for ‘perfect cube’ yields only 11 primes for the same range of n. Hence, sequence for ‘square’ is framed.

Subsequence of primes of A066564. - Michel Marcus, Jun 02 2015

			a(2) = 17 is prime. Digit sum of 17 = 8, 17 + 8 = 25 = 5^2.
a(5) = 467 is prime. Digit sum of 467 = 17, 467 + 17 = 484 = 22^2.

K. D. Bajpai and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (terms 2..150 from Bajpai)

Cf. A048519.

Cf. A107288 (Primes whose digit sum is square).

[p: p in PrimesUpTo(6*10^5) | IsSquare(p+(&+Intseq(p)))]; // Vincenzo Librandi, Jun 02 2015

KD:= proc() local a,b,c,d; a:= ithprime(n);b:=add( i,i = convert((a), base, 10))(a); c:=a+b; d:=evalf(sqrt(c)); if d=floor(d) then return (a) :fi;end:seq(KD(),n=1..50000);

for(n=2,1e4,forprime(p=n^2-9*#digits(n^2),n^2, if(p+sumdigits(p) == n^2, print1(p", ")))) \\ Charles R Greathouse IV, Oct 08 2013

a(1) from Charles R Greathouse IV, Oct 08 2013

A362069 Numbers k such that k+digitsum(k^2) is a square.

Original entry on oeis.org

0, 17, 62, 71, 117, 125, 197, 206, 296, 297, 305, 413, 414, 557, 558, 692, 702, 711, 863, 864, 872, 873, 1062, 1070, 1071, 1268, 1493, 1502, 1727, 1736, 1737, 1745, 1998, 2006, 2267, 2276, 2285, 2564, 2565, 2573, 2879, 2888, 2889, 3221, 3222

Offset: 1

Alexandru Petrescu, May 17 2023

Conjecture: there are infinitely many pairs of consecutive terms. Example: (296,297); (413,414); (863,864).

			k=17 is a term because k^2=289 and 17+2+8+9=36=6^2.

Cf. A004159, A066564.

Select[Range[0, 3300], IntegerQ[Sqrt[# + Plus @@ IntegerDigits[#^2]]] &] (* Amiram Eldar, May 18 2023 *)

PARI
```
isok(k)=issquare(k+sumdigits(k^2))
```

cp's OEIS Frontend

A062028 a(n) = n + sum of the digits of n.

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A066566 Numbers that when decremented by the sum of their digits produce a square.

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A066567 Numbers that when incremented by the product of their digits produce a square.

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A084661 Numbers k such that k + sum_of_digits(k) is a cube.

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A230087 Primes such that prime plus its digit sum is a perfect square.

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Magma

Maple

PARI

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A362069 Numbers k such that k+digitsum(k^2) is a square.

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Author

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Comments

Examples

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Programs

Mathematica

PARI