A010807 -id:A010807 - cp's OEIS frontend

A247894 Integer part of square root of A010807: a(n) = floor(sqrt(n^19)).

0, 1, 724, 34091, 524288, 4367320, 24685212, 106765608, 379625062, 1162261467, 3162277660, 7820427766, 17874003451, 38235066239, 77306558317, 148890490631, 274877906944, 488950340714, 841567195983, 1406563064942, 2289733608959, 3639848436450, 5662594565481

Offset: 0

Karl V. Keller, Jr., Sep 27 2014

nonn

a(n) = A000196(A010807(n)). - Reinhard Zumkeller, Sep 29 2014

Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 201 terms from Karl V. Keller, Jr.)

Cf. A010807 (n^19).

Cf. A000196.

a247894 = a000196 . a010807  -- Reinhard Zumkeller, Sep 29 2014

seq(floor(sqrt(n^19)),n=0..100); # Robert Israel, Sep 28 2014

a(n) = sqrtint(n^19); \\ Michel Marcus, Sep 28 2014

a(n) = floor(sqrt(n^19)).

A170801 a(n) = n^10*(n^9 + 1)/2.

Original entry on oeis.org

0, 1, 262656, 581160258, 137439477760, 9536748046875, 304679900238336, 5699447733924196, 72057594574798848, 675425860579888245, 5000000005000000000, 30579545237175985446, 159739999716270145536

Offset: 0

N. J. A. Sloane, Dec 11 2009

Number of unoriented rows of length 19 using up to n colors. For a(0)=0, there are no rows using no colors. For a(1)=1, there is one row using that one color for all positions. For a(2)=262656, there are 2^19=524288 oriented arrangements of two colors. Of these, 2^10=1024 are achiral. That leaves (524288-1024)/2=261632 chiral pairs. Adding achiral and chiral, we get 262656. - Robert A. Russell, Nov 13 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (20, -190, 1140, -4845, 15504, -38760, 77520, -125970, 167960, -184756, 167960, -125970, 77520, -38760, 15504, -4845, 1140, -190, 20, -1).

Row 19 of A277504.
Cf. A010807 (oriented), A008454 (achiral).
Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170796 (m=4), A170797 (m=5), A170798 (m=6), A170799 (m=7), A170800 (m=8), this sequence (m=9), A170802 (m=10).

List([0..30], n -> n^10*(n^9+1)/2); # G. C. Greubel, Nov 15 2018

[n^10*(n^9+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

seq(n^10*(n^9 +1)/2, n=0..20); # G. C. Greubel, Oct 11 2019

Table[(n^19 + n^10)/2, {n,0,30}] (* Robert A. Russell, Nov 13 2018 *)

vector(30, n, n--; n^10*(n^9+1)/2) \\ G. C. Greubel, Nov 15 2018

[n^10*(n^9+1)/2 for n in range(30)] # G. C. Greubel, Nov 15 2018

From Robert A. Russell, Nov 13 2018: (Start)
a(n) = (A010807(n) + A008454(n)) / 2 = (n^19 + n^10) / 2.
G.f.: (Sum_{j=1..19} S2(19,j)*j!*x^j/(1-x)^(j+1) + Sum_{j=1..10} S2(10,j)*j!*x^j/(1-x)^(j+1)) / 2, where S2 is the Stirling subset number A008277.
G.f.: x*Sum_{k=0..18} A145882(19,k) * x^k / (1-x)^20.
E.g.f.: (Sum_{k=1..19} S2(19,k)*x^k + Sum_{k=1..10} S2(10,k)*x^k) * exp(x) / 2, where S2 is the Stirling subset number A008277.
For n>19, a(n) = Sum_{j=1..20} -binomial(j-21,j) * a(n-j). (End)

A010810 22nd powers: a(n) = n^22.

Original entry on oeis.org

0, 1, 4194304, 31381059609, 17592186044416, 2384185791015625, 131621703842267136, 3909821048582988049, 73786976294838206464, 984770902183611232881, 10000000000000000000000, 81402749386839761113321

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (23, -253, 1771, -8855, 33649, -100947, 245157, -490314, 817190, -1144066, 1352078, -1352078, 1144066, -817190, 490314, -245157, 100947, -33649, 8855, -1771, 253, -23, 1).

Cf. A010807, A013678, A010809.

[n^22: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011

Table[n^20, {n, 0, 22}] (* Amiram Eldar, Oct 09 2020 *)

a(n) = n^22; \\ Michel Marcus, Feb 27 2018

Totally multiplicative sequence with a(p) = p^22 for prime p. Multiplicative sequence with a(p^e) = p^(22e). - Jaroslav Krizek, Nov 01 2009
From Amiram Eldar, Oct 09 2020: (Start)
Dirichlet g.f.: zeta(s-22).
Sum_{n>=1} 1/a(n) = zeta(22) = 155366*Pi^22/13447856940643125.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2097151*zeta(22)/2097152 = 3324754717*Pi^22/287777551824322560000. (End)

A036097 Centered cube numbers: (n+1)^19+n^19.

Original entry on oeis.org

1, 524289, 1162785755, 276040168411, 19348364235069, 628433226338621, 12008254925383639, 155514083261229015, 1494966905748847961, 11350851717672992089, 71159090448414546291, 380639089819037473139, 1781400289746069037525, 7438224249324360507861

Offset: 0

N. J. A. Sloane

Never prime, as a(n) = (2n + 1) * (n^18 + 9n^17 + 81n^16 + 444n^15 + 1716n^14 + 4956n^13 + 11088n^12 + 19650n^11 + 27966n^10 + 32206n^9 + 30086n^8 + 22748n^7 + 13820n^6 + 6656n^5 + 2486n^4 + 695n^3 + 137n^2 + 17n + 1). Semiprime for n in {1, 3, 8, 39, 41, 54, 111, 119, 141 ...}. [Jonathan Vos Post, Aug 27 2011]

Sums of consecutive pairs of terms of A010807. - Wesley Ivan Hurt, Jul 13 2014

			1^19 + (1+1)^19 = 524289 = 3 * 174763, a semiprime.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Cf. A010807, A036096, A036096.

[(n+1)^19+n^19: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011

A036097:=n->(n+1)^19+n^19: seq(A036097(n), n=0..20); # Wesley Ivan Hurt, Jul 13 2014

Total/@Partition[Range[0,20]^19,2,1] (* Harvey P. Dale, Mar 04 2013 *)
f[n_] := n^19; Array[f[#] + f[# + 1] &, 14, 0] (* Robert G. Wilson v, Jul 22 2014 *)

a(n) = A010807(n+1) + A010807(n). - Wesley Ivan Hurt, Jul 13 2014

A022535 Nexus numbers (n+1)^19 - n^19.

Original entry on oeis.org

1, 524287, 1161737179, 273715645477, 18798608421181, 590286253682371, 10789535445362647, 132716292890482729, 1206736529597136217, 8649148282327007911, 51159090448414546291, 258320908922208380557, 1142440291004823183829, 4514383668573468286507, 16192074241582091462191

Offset: 0

N. J. A. Sloane

J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Column k=18 of A047969.

Cf. A010807 (n^19).

[(n+1)^19-n^19: n in [0..20]]; // Vincenzo Librandi, Nov 22 2011

b:=19: a:=n->(n+1)^b-n^b: seq(a(n),n=0..18); # Muniru A Asiru, Feb 28 2018

Table[(n+1)^19-n^19,{n,0,20}] (* Vincenzo Librandi, Nov 22 2011 *)

for(n=0,20, print1((n+1)^19 - n^19, ", ")) \\ G. C. Greubel, Feb 27 2018

a(n) = A010807(n+1) - A010807(n). - Michel Marcus, Feb 28 2018

More terms added by G. C. Greubel, Feb 27 2018

cp's OEIS Frontend

A247894 Integer part of square root of A010807: a(n) = floor(sqrt(n^19)).

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A170801 a(n) = n^10*(n^9 + 1)/2.

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A010810 22nd powers: a(n) = n^22.

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A036097 Centered cube numbers: (n+1)^19+n^19.

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A022535 Nexus numbers (n+1)^19 - n^19.

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