A008588 -id:A008588 - cp's OEIS frontend

A044102 Multiples of 36.

0, 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, 468, 504, 540, 576, 612, 648, 684, 720, 756, 792, 828, 864, 900, 936, 972, 1008, 1044, 1080, 1116, 1152, 1188, 1224, 1260, 1296, 1332, 1368, 1404, 1440, 1476, 1512, 1548, 1584, 1620, 1656, 1692, 1728

Offset: 0

Clark Kimberling

Also, k such that Fibonacci(k) mod 27 = 0. - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 18 2004
A033183(a(n)) = n+1. - Reinhard Zumkeller, Nov 07 2009
A122841(a(n)) > 1 for n > 0. - Reinhard Zumkeller, Nov 10 2013
Sum of the numbers from 4*(n-1) to 4*(n+1). - Bruno Berselli, Oct 25 2018

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A005843, A008600, A033183, A122841, A135631, A167632, A174312.

Subsequence of A008588.

a:=[0,36];; for n in [3..50] do a[n]:=2*a[n-1]-a[n-2]; od; a; # Muniru A Asiru, Oct 25 2018

a044102 = (* 36)
a044102_list = [0, 36 ..]  -- Reinhard Zumkeller, Nov 10 2013

[36*n: n in [0..50]]; // Vincenzo Librandi, May 20 2014

seq(coeff(series(36*x/(1-x)^2,x,n+1), x, n), n = 0 .. 50); # Muniru A Asiru, Oct 25 2018

Range[0, 2000, 36] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)
CoefficientList[Series[36 x/(1 - x)^2, {x, 0, 100}], x] (* Vincenzo Librandi, May 20 2014 *)

a(n)=36*n \\ Charles R Greathouse IV, Oct 07 2015

G.f.: 36*x/(1 - x)^2.
a(n) = A167632(n+1). - Reinhard Zumkeller, Nov 07 2009
a(n) = 36*n. - Vincenzo Librandi, Jan 26 2011
From Elmo R. Oliveira, Apr 10 2025: (Start)
E.g.f.: 36*x*exp(x).
a(n) = 18*A005843(n) = 2*A008600(n).
a(n) = 2*a(n-1) - a(n-2). (End)

A057355 a(n) = floor(3*n/5).

Original entry on oeis.org

0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 40, 41, 42, 42, 43, 43

Offset: 0

Mitch Harris

The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.

The sequence can be obtained from A008588 by deleting the last digit of each term. - Bruno Berselli, Sep 11 2019

N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, NY, 1994.

G. C. Greubel, Table of n, a(n) for n = 0..5000
N. Dershowitz and E. M. Reingold, Calendrical Calculations Web Site.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.

Cf. A008588.

[3*n div 5: n in [0..80]]; // Bruno Berselli, Dec 07 2016

Table[Floor[3*n/5], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *)

a(n)=3*n\5 \\ Charles R Greathouse IV, Sep 02 2015

G.f.: x^2*(1 + x^2 + x^3)/((1 - x)*(1 - x^5)). - Bruce Corrigan (scentman(AT)myfamily.com), Jul 03 2002
For all m>=0: a(5m)=0 mod 3; a(5m+1)=0 mod 3; a(5m+2)=1 mod 3; a(5m+3)=1 mod 3; a(5m+4)=2 mod 3.
Sum_{n>=2} (-1)^n/a(n) = Pi/(3*sqrt(3)) - log(2)/3. - Amiram Eldar, Sep 30 2022

A063265 Septinomial (also called heptanomial) coefficient array.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 1, 3, 6, 10, 15, 21, 28, 33, 36, 37, 36, 33, 28, 21, 15, 10, 6, 3, 1, 1, 4, 10, 20, 35, 56, 84, 116, 149, 180, 206, 224, 231, 224, 206, 180, 149, 116, 84, 56, 35

Offset: 0

Wolfdieter Lang, Jul 24 2001

The sequence of step width of this staircase array is [1,6,6,...], hence the degree sequence for the row polynomials is [0,6,12,18,...]= A008588.

The column sequences (without leading zeros) are for k=0..6 those of the lower triangular array A007318 (Pascal) and for k=7..9: A063267, A063417, A063418. Row sums give A000420 (powers of 7). Central coefficients give A025012.

			Triangle begins:
  {1};
  {1, 1, 1, 1, 1, 1, 1};
  {1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1};
  ...
N7(k,x)= 1 for k=0..6, N7(7,x)= 6-15*x+20*x^2-15*x^3+6*x^4-x^5 (from A063266).

L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 77,78.

T. D. Noe, Rows n = 0..25, flattened
Steven R. Finch, P. Sebah and Z.-Q. Bai, Odd Entries in Pascal's Trinomial Triangle, arXiv:0802.2654 [math.NT], 2008.

The q-nomial arrays are for q=2..8: A007318 (Pascal), A027907, A008287, A035343, A063260, A063265, A171890.

#Define the r-nomial coefficients for r = 1, 2, 3, ...
rnomial := (r,n,k) -> add((-1)^i*binomial(n,i)*binomial(n+k-1-r*i,n-1), i = 0..floor(k/r)):
#Display the 7-nomials as a table
r := 7:  rows := 10:
for n from 0 to rows do
seq(rnomial(r,n,k), k = 0..(r-1)*n)
end do;
# Peter Bala, Sep 07 2013

Flatten[Table[CoefficientList[(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)^n, x], {n, 0, 25}]] (* T. D. Noe, Apr 04 2011 *)

a(n, k)=0 if n=-1 or k<0 or k >= 6*n; a(0, 0)=1; a(n, k)= sum(a(n-1, k-j), j=0..6) else.
G.f. for row n: (sum(x^j, j=0..6))^n.
G.f. for column k: (x^(ceiling(k/6)))*N7(k, x)/(1-x)^(k+1) with the row polynomials of the staircase array A063266(k, m).
T(n,k) = Sum_{i = 0..floor(k/7)} (-1)^i*binomial(n,i)*binomial(n+k-1-7*i,n-1) for n >= 0 and 0 <= k <= 6*n. - Peter Bala, Sep 07 2013

A119313 Numbers with a prime as third-smallest divisor.

Original entry on oeis.org

6, 10, 12, 14, 15, 18, 21, 22, 24, 26, 30, 33, 34, 35, 36, 38, 39, 42, 45, 46, 48, 50, 51, 54, 55, 57, 58, 60, 62, 63, 65, 66, 69, 70, 72, 74, 75, 77, 78, 82, 84, 85, 86, 87, 90, 91, 93, 94, 95, 96, 98, 102, 105, 106, 108, 110, 111, 114, 115, 118, 119, 120, 122, 123, 126

Offset: 1

Reinhard Zumkeller, May 15 2006

nonn

m is a term iff A001221(m) > 1 and (A067029(m) = 1 or A119288(m) < A020639(m)^2).

			a(1) = A087134(3) = 6.
From _Gus Wiseman_, Oct 19 2019: (Start)
The sequence of terms together with their divisors begins:
    6: {1,2,3,6}
   10: {1,2,5,10}
   12: {1,2,3,4,6,12}
   14: {1,2,7,14}
   15: {1,3,5,15}
   18: {1,2,3,6,9,18}
   21: {1,3,7,21}
   22: {1,2,11,22}
   24: {1,2,3,4,6,8,12,24}
   26: {1,2,13,26}
   30: {1,2,3,5,6,10,15,30}
   33: {1,3,11,33}
   34: {1,2,17,34}
   35: {1,5,7,35}
   36: {1,2,3,4,6,9,12,18,36}
   38: {1,2,19,38}
   39: {1,3,13,39}
   42: {1,2,3,6,7,14,21,42}
   45: {1,3,5,9,15,45}
   46: {1,2,23,46}
(End)

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Complement of A119314.
Subsequences: A006881, A000469, A008588.
A subset of A002808 and A080257.
Numbers whose third-largest divisor is prime are A328338.
Second-smallest divisor is A020639.
Third-smallest divisor is A292269.
Cf. A000005, A000040, A001221, A020639, A027750, A033676, A060775, A067029, A088725, A119288, A328189.

q:= n-> (l-> nops(l)>2 and isprime(l[3]))(
         sort([numtheory[divisors](n)[]])):
select(q, [$1..200])[];  # Alois P. Heinz, Oct 19 2019

Select[Range[100],Length[Divisors[#]]>2&&PrimeQ[Divisors[#][[3]]]&] (* Gus Wiseman, Oct 15 2019 *)
Select[Range[130], Length[f = FactorInteger[#]] > 1 && (f[[1, 2]] == 1 || f[[1, 1]]^2 > f[[2, 1]]) &] (* Amiram Eldar, Jul 02 2022 *)

Name edited by Gus Wiseman, Oct 19 2019

A134492 a(n) = Fibonacci(6*n).

Original entry on oeis.org

0, 8, 144, 2584, 46368, 832040, 14930352, 267914296, 4807526976, 86267571272, 1548008755920, 27777890035288, 498454011879264, 8944394323791464, 160500643816367088, 2880067194370816120, 51680708854858323072, 927372692193078999176, 16641027750620563662096

Offset: 0

Artur Jasinski, Oct 28 2007

All terms are divisible by 8. - Alonso del Arte, Jul 27 2013

Conjecture: For n >= 2, the terms of this sequence are exactly those Fibonacci numbers which are the sum of the three numbers of a Pythagorean triple (checked up to F(80)). - Felix Huber, Nov 03 2023

Colin Barker, Table of n, a(n) for n = 0..500
Hacène Belbachir, Soumeya Merwa Tebtoub and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
Index entries for linear recurrences with constant coefficients, signature (18,-1).

Cf. A000032, A000045, A008588, A049660, A079343, A014445, A014448, A134493, A134494, A134495, A103134, A134497, A134498.

[Fibonacci(6*n): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011

Table[Fibonacci[6n], {n, 0, 30}]
LinearRecurrence[{18,-1},{0,8},30] (* Harvey P. Dale, Aug 15 2017 *)

numlib::fibonacci(6*n) $ n = 0..25; // Zerinvary Lajos, May 09 2008

a(n)=fibonacci(6*n) \\ Charles R Greathouse IV, Sep 16 2015

concat(0, Vec(8*x/(1-18*x+x^2) + O(x^20))) \\ Colin Barker, Jan 24 2016

[fibonacci(6*n) for n in range(0, 17)] # Zerinvary Lajos, May 15 2009

a(n) = 18*a(n-1) - a(n-2) = 8*A049660(n). G.f.: 8*x/(1-18*x+x^2). - R. J. Mathar, Feb 16 2010
a(n) = A000045(A008588(n)). - Michel Marcus, Nov 08 2013
a(n) = ((-1+(9+4*sqrt(5))^(2*n)))/(sqrt(5)*(9+4*sqrt(5))^n). - Colin Barker, Jan 24 2016
a(n) = L(2n-1) * F(2n+1)^2 + L(2n+1) * F(2n-1)^2, where F(n) = A000045(n) and L(n) = A000032(n). - Diego Rattaggi, Nov 12 2020
a(n) = Fibonacci(3*n) * Lucas(3*n) = A000045(3*n) * A000032(3*n) = A014445(n) * A014448(n). - Amiram Eldar, Jan 11 2022

Offset corrected by R. J. Mathar, Feb 16 2010

A276378 Numbers k such that 6*k is squarefree.

Original entry on oeis.org

1, 5, 7, 11, 13, 17, 19, 23, 29, 31, 35, 37, 41, 43, 47, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 127, 131, 133, 137, 139, 143, 145, 149, 151, 155, 157, 161, 163, 167, 173, 179, 181, 185, 187, 191, 193, 197, 199, 203, 205, 209, 211

Offset: 1

Juri-Stepan Gerasimov, Sep 02 2016

These are the numbers from A005117 that are not divisible by 2 and 3.
Squarefree numbers coprime to 6. - Robert Israel, Sep 02 2016
Numbers k such that A008588(k) is in A005117. - Felix Fröhlich, Sep 02 2016
The asymptotic density of this sequence is 3/Pi^2 (A104141). - Amiram Eldar, May 22 2020
From Peter Munn, Nov 20 2020: (Start)
The products generated from each subset of A215848 (primes greater than 3).
Closed under the commutative binary operation A059897(.,.), forming a subgroup of the positive integers under A059897. (End)
Multiplied by 6 we have 6, 30, 42, 66, 78, 102, ..., the values that may appear in A076978 after the 1, 2. [Don Reble, Dec 02 2020] - R. J. Mathar, Dec 15 2020
By the von Staudt-Clausen theorem, denominators of Bernoulli numbers are of the form 6*a(n) for some n. - Charles R Greathouse IV, May 16 2024

			5 is in this sequence because 6*5 = 30 = 2*3*5 is squarefree.

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

Numbers m such that k*m is squarefree: A005117 (k = 1), A056911 (k = 2), A261034 (k = 3), A274546 (k = 5).
Subsequence of A007310, A300957, and A339690.
Cf. A003961, A008588, A059897, A076978, A104141, A215848.

[n: n in [1..230] | IsSquarefree(6*n)];

select(numtheory:-issqrfree, [seq(seq(6*i+j,j=[1,5]),i=0..100)]); # Robert Israel, Sep 02 2016

Select[Range@ 212, SquareFreeQ[6 #] &] (* Michael De Vlieger, Sep 02 2016 *)

is(n) = issquarefree(6*n) \\ Felix Fröhlich, Sep 02 2016

{a(n) : n >= 1} = {A003961(A003961(A005117(n))) : n >= 1} = {A003961(A056911(n)) : n >= 1}. - Peter Munn, Nov 20 2020

Sum_{n>=1} 1/a(n)^s = (6^s)*zeta(s)/((1+2^s)*(1+3^s)*zeta(2*s)), s>1. - Amiram Eldar, Sep 26 2023

A046953 Numbers k such that 6*k - 1 is composite.

Original entry on oeis.org

6, 11, 13, 16, 20, 21, 24, 26, 27, 31, 34, 35, 36, 37, 41, 46, 48, 50, 51, 54, 55, 56, 57, 61, 62, 63, 66, 68, 69, 71, 73, 76, 79, 81, 83, 86, 88, 89, 90, 91, 92, 96, 97, 101, 102, 104, 105, 106, 111, 112, 115, 116, 118, 119, 121, 122, 123, 125, 126, 128

Offset: 1

Felice Russo

nonn

These numbers can be written as 6*x*y + x - y for x > 0, y > 0. - Ron R Spencer, Aug 01 2016

			a(1)=6 because 6*6 - 1 = 35, which is composite.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A046954, A008588, A016969, subsequence of A067611.

Cf. A024898 (complement).

Filtered([1..200], k-> not IsPrime(6*k-1)) # G. C. Greubel, Feb 21 2019

a046953 n = a046953_list !! (n-1)
a046953_list = map (`div` 6) $
   filter ((== 0) . a010051' . subtract 1) [6,12..]
-- Reinhard Zumkeller, Jul 13 2014

[n: n in [1..200] | not IsPrime(6*n-1)]; // G. C. Greubel, Feb 21 2019

remove(k-> isprime(6*k-1), [$1..130])[]; # Muniru A Asiru, Feb 22 2019

Select[Range[200],!PrimeQ[6#-1]&] (* Vladimir Joseph Stephan Orlovsky, Feb 25 2011 *)

is(n)=!isprime(6*n-1) \\ Charles R Greathouse IV, Aug 01 2016

[n for n in (1..200) if not is_prime(6*n-1)] # G. C. Greubel, Feb 21 2019

a(n) ~ n. - Charles R Greathouse IV, Aug 01 2016

A135628 Multiples of 28.

Original entry on oeis.org

0, 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, 364, 392, 420, 448, 476, 504, 532, 560, 588, 616, 644, 672, 700, 728, 756, 784, 812, 840, 868, 896, 924, 952, 980, 1008, 1036, 1064, 1092, 1120, 1148, 1176, 1204, 1232, 1260, 1288, 1316, 1344, 1372

Offset: 0

Omar E. Pol, Nov 25 2007

			a(9) = 28*9 = 252.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014.
Index entries for linear recurrences with constant coefficients, signature (2,-1)

Cf. A008588, A008596, A127777.

Range[0, 3000, 28] (* Vladimir Joseph Stephan Orlovsky, Jun 03 2011 *)
LinearRecurrence[{2,-1},{0,28},25] (* G. C. Greubel, Oct 24 2016 *)

a(n) = 28*n.
From G. C. Greubel, Oct 24 2016: (Start)
G.f.: (28*x)/(1 - x)^2.
E.g.f.: 28*x*exp(x).
a(n) = 2*a(n-1) - a(n-2). (End)

A346875 Irregular triangle read by rows in which row n lists the row A000384(n) of A237591, n >= 1.

Original entry on oeis.org

1, 4, 1, 1, 8, 3, 2, 1, 1, 15, 5, 3, 2, 1, 1, 1, 23, 8, 5, 2, 2, 2, 1, 1, 1, 34, 11, 6, 4, 3, 2, 2, 1, 1, 1, 1, 46, 16, 8, 5, 4, 2, 3, 1, 2, 1, 1, 1, 1, 61, 20, 11, 6, 5, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 77, 26, 14, 8, 5, 5, 3, 2, 3, 2, 1, 2, 1, 1, 1, 1, 1, 96, 32, 16

Offset: 1

Omar E. Pol, Aug 06 2021

The characteristic shape of the symmetric representation of sigma(A000384(n)) consists in that in the main diagonal of the diagram the smallest Dyck path has a valley and the largest Dyck path has a peak.
So knowing this we can know if a number is a hexagonal number (or not) just by looking at the diagram, even ignoring the concept of hexagonal number.
Therefore we can see a geometric pattern of the distribution of the hexagonal numbers in the stepped pyramid described in A245092.
T(n,k) is also the length of the k-th line segment of the largest Dyck path of the symmetric representation of sigma(A000384(n-1)), from the border to the center, hence the sum of the n-th row of triangle is equal to A000384(n-1).
T(n,k) is also the difference between the total number of partitions of all positive integers <= n-th hexagonal number into exactly k consecutive parts, and the total number of partitions of all positive integers <= n-th hexagonal number into exactly k + 1 consecutive parts.

			Triangle begins:
   1;
   4,  1,  1;
   8,  3,  2,  1, 1;
  15,  5,  3,  2, 1, 1, 1;
  23,  8,  5,  2, 2, 2, 1, 1, 1;
  34, 11,  6,  4, 3, 2, 2, 1, 1, 1, 1;
  46, 16,  8,  5, 4, 2, 3, 1, 2, 1, 1, 1, 1;
  61, 20, 11,  6, 5, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1;
  77, 26, 14,  8, 5, 5, 3, 2, 3, 2, 1, 2, 1, 1, 1, 1, 1;
  96, 32, 16, 10, 7, 5, 4, 3, 3, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1;
...
Illustration of initial terms:
Column H gives the nonzero hexagonal numbers (A000384).
Column S gives the sum of the divisors of the hexagonal numbers which equals the area (and the number of cells) of the associated diagram.
-------------------------------------------------------------------------
  n    H    S   Diagram
-------------------------------------------------------------------------
                 _         _                 _                         _
  1    1    1   |_|       | |               | |                       | |
                 1        | |               | |                       | |
                       _ _| |               | |                       | |
                      |    _|               | |                       | |
                 _ _ _|  _|                 | |                       | |
  2    6   12   |_ _ _ _| 1                 | |                       | |
                    4    1                  | |                       | |
                                       _ _ _|_|                       | |
                                   _ _| |                             | |
                                  |    _|                             | |
                                 _|  _|                               | |
                                |_ _|1 1                              | |
                                | 2                                   | |
                 _ _ _ _ _ _ _ _|4                           _ _ _ _ _| |
  3   15   24   |_ _ _ _ _ _ _ _|                           |  _ _ _ _ _|
                        8                                   | |
                                                         _ _| |
                                                     _ _|  _ _|
                                                    |    _|
                                                   _|  _|
                                                  |  _|1 1
                                             _ _ _| | 1
                                            |  _ _ _|2
                                            | |  3
                                            | |
                                            | |5
                 _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
  4   28   56   |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
                              15
.

Row sums give A000384, n >= 1.
Row lengths give A005408.
Column 1 is A267682, n >= 1.
For the characteristic shape of sigma(A000040(n)) see A346871.
For the characteristic shape of sigma(A000079(n)) see A346872.
For the characteristic shape of sigma(A000217(n)) see A346873.
For the visualization of Mersenne numbers A000225 see A346874.
For the characteristic shape of sigma(A000396(n)) see A346876.
For the characteristic shape of sigma(A008588(n)) see A224613.
Cf. A000203, A237591, A237593, A245092, A249351, A262626.

A008881 a(n) = Product_{j=0..5} floor((n+j)/6).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 2, 4, 8, 16, 32, 64, 96, 144, 216, 324, 486, 729, 972, 1296, 1728, 2304, 3072, 4096, 5120, 6400, 8000, 10000, 12500, 15625, 18750, 22500, 27000, 32400, 38880, 46656, 54432, 63504, 74088, 86436, 100842, 117649, 134456, 153664, 175616, 200704

Offset: 0

N. J. A. Sloane

For n >= 6, a(n) is the maximal product of 6 positive integers with sum n. - Wesley Ivan Hurt, Jun 29 2022

The maximal product of k positive variables when their sum is equal to s is obtained when each term = s/k; hence, a(6m) = m^6 (A001014). - Bernard Schott, Jul 28 2022

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,5,-10,5,0,0,0,-10,20,-10,0,0,0,10,-20,10,0,0,0,-5,10,-5,0,0,0,1,-2,1).

Maximal product of k positive integers with sum n, for k = 2..10: A002620 (k=2), A006501 (k=3), A008233 (k=4), A008382 (k=5), this sequence (k=6), A009641 (k=7), A009694 (k=8), A009714 (k=9), A354600 (k=10).

Cf. A001014 (6th power), A008588 (multiples of 6), A013664.

List([0..50], n-> Product([0..5], j-> Int((n+j)/6))); # G. C. Greubel, Sep 13 2019

[(&*[Floor((n+j)/6): j in [0..5]]): n in [0..50]]; // G. C. Greubel, Sep 13 2019

seq( mul( floor((n+i)/6), i=0..5 ), n=0..80);

Product[Floor[(Range[51]+j-2)/6], {j,6}] (* G. C. Greubel, Sep 13 2019 *)

vector(50, n, prod(j=0,5, (n+j)\6) ) \\ G. C. Greubel, Sep 13 2019

[product(floor((n+j)/6) for j in (0..5)) for n in (0..50)] # G. C. Greubel, Sep 13 2019

Sum_{n>=6} 1/a(n) = 1 + zeta(6). - Amiram Eldar, Jan 10 2023

cp's OEIS Frontend

A044102 Multiples of 36.

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Haskell

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A057355 a(n) = floor(3*n/5).

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A063265 Septinomial (also called heptanomial) coefficient array.

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Maple

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A119313 Numbers with a prime as third-smallest divisor.

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A134492 a(n) = Fibonacci(6*n).

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A276378 Numbers k such that 6*k is squarefree.

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Magma