A305548 -id:A305548 - cp's OEIS frontend

A244634 a(n) = 27*n^2.

0, 27, 108, 243, 432, 675, 972, 1323, 1728, 2187, 2700, 3267, 3888, 4563, 5292, 6075, 6912, 7803, 8748, 9747, 10800, 11907, 13068, 14283, 15552, 16875, 18252, 19683, 21168, 22707, 24300, 25947, 27648, 29403, 31212, 33075, 34992, 36963, 38988, 41067, 43200, 45387

Offset: 0

Vincenzo Librandi, Jul 03 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. similar sequences listed in A244630.

Cf. A000290, A016766, A033428, A305548.

Magma
```
[27*n^2: n in [0..40]];
```
Mathematica
```
Table[27 n^2, {n, 0, 40}]
```

a(n)=27*n^2 \\ Charles R Greathouse IV, Jun 17 2017

G.f.: 27*x*(1 + x)/(1 - x)^3. [corrected by Bruno Berselli, Jul 03 2014]
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
a(n) = 27*A000290(n) = 9*A033428(n) = 3*A016766(n). - Omar E. Pol, Jul 03 2014
From Elmo R. Oliveira, Dec 01 2024: (Start)
E.g.f.: 27*x*(1 + x)*exp(x).
a(n) = n*A305548(n). (End)

A306824 Integer k such that digsum(k) = digsum (k/p(1)) = digsum (k/p(2)) = ... for all prime factors p(i) of k, where digsum(k) = A007953(k) is the digital sum of k.

Original entry on oeis.org

1, 27, 54, 81, 108, 135, 162, 216, 243, 270, 324, 351, 361, 405, 432, 513, 540, 621, 702, 703, 810, 1026, 1053, 1080, 1215, 1242, 1458, 1620, 1728, 1944, 2071, 2079, 2106, 2133, 2160, 2187, 2403, 2413, 2592, 2700, 2701, 2916, 3024, 3051, 3105, 3267, 3321, 4023, 4033, 4050, 4158

Offset: 1

Michel Lagneau, Mar 12 2019

a(n) == 0 or 1 (mod 9). If a(n) == 0 (mod 9), a(n) == 0 (mod 27).

			4158 = 2*3^3*7*11 is in the sequence because 4 + 1 + 5 + 8 = 18, and:
4158/2 = 2079 and digsum(2079) = 18;
4158/3 = 1386 and digsum(1386) = 18;
4158/7 = 594 and digsum(594) = 18;
4158/11 = 378 and digsum(378) = 18.

Cf. A007953, A305548, A306761 (a subsequence).

with(numtheory):nn:=4200:
  for k from 1 to nn do:
     d:=factorset(k):n1:=nops(d):it:=0:
     b:=convert(k, base, 10):n2:=nops(b):s:=sum(‘b[i]’, ‘i’=1..n2):
      for i from 1 to n1 do:
        x:=k/d[i]:b1:=convert(x, base, 10):n3:=nops(b1):
        s1:=sum(‘b1[i]’, ‘i’=1..n3):
        if s1=s
         then
         it:=it+1:
         else
        fi:
      od:
       if it=n1
        then
        printf(`%d, `,k):
       else
      fi:
od:

sod[n_] := Total@IntegerDigits@n; Select[Range[1, 5000], {sod[#]} == Union[sod /@ (#/First /@ FactorInteger[#])] &] (* Giovanni Resta, Mar 12 2019 *)

isok(k) = {my(pf = factor(k)[,1]~, sd = sumdigits(k)); for (i=1, #pf, if (sumdigits(k/pf[i]) != sd, return (0));); return (1);} \\ Michel Marcus, Mar 12 2019

cp's OEIS Frontend

A244634 a(n) = 27*n^2.

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