A010813 -id:A010813 - cp's OEIS frontend

A248132 Integer part of square root of A010813(n) = n^25.

0, 1, 5792, 920482, 33554432, 545915033, 5332006004, 36620603758, 194368031998, 847288609443, 3162277660168, 10408989356987, 30886277963534, 84002440529229, 212129196024140, 502505405881790, 1125899906842624

Offset: 0

Karl V. Keller, Jr., Oct 02 2014

nonn

			For n = 4, floor(sqrt(n^25)) = 33554432.

Karl V. Keller, Jr., Table of n, a(n) for n = 0..1000

Cf. A010813 (n^25).

Table[Floor[Sqrt[n^25]],{n,0,20}] (* Harvey P. Dale, Aug 27 2017 *)

from math import isqrt
print([isqrt(n**25) for n in range(0, 21)])

a(n) = floor(sqrt(n^25)).

A003992 Square array read by upwards antidiagonals: T(n,k) = n^k for n >= 0, k >= 0.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 4, 1, 0, 1, 4, 9, 8, 1, 0, 1, 5, 16, 27, 16, 1, 0, 1, 6, 25, 64, 81, 32, 1, 0, 1, 7, 36, 125, 256, 243, 64, 1, 0, 1, 8, 49, 216, 625, 1024, 729, 128, 1, 0, 1, 9, 64, 343, 1296, 3125, 4096, 2187, 256, 1, 0, 1, 10, 81, 512, 2401, 7776, 15625, 16384, 6561, 512, 1, 0

Offset: 0

Marc LeBrun

If the array is transposed, T(n,k) is the number of oriented rows of n colors using up to k different colors. The formula would be T(n,k) = [n==0] + [n>0]*k^n. The generating function for column k would be 1/(1-k*x). For T(3,2)=8, the rows are AAA, AAB, ABA, ABB, BAA, BAB, BBA, and BBB. - Robert A. Russell, Nov 08 2018

T(n,k) is the number of multichains of length n from {} to [k] in the Boolean lattice B_k. - Geoffrey Critzer, Apr 03 2020

			Rows begin:
[1, 0,  0,   0,    0,     0,      0,      0, ...],
[1, 1,  1,   1,    1,     1,      1,      1, ...],
[1, 2,  4,   8,   16,    32,     64,    128, ...],
[1, 3,  9,  27,   81,   243,    729,   2187, ...],
[1, 4, 16,  64,  256,  1024,   4096,  16384, ...],
[1, 5, 25, 125,  625,  3125,  15625,  78125, ...],
[1, 6, 36, 216, 1296,  7776,  46656, 279936, ...],
[1, 7, 49, 343, 2401, 16807, 117649, 823543, ...], ...

T. D. Noe, Rows n = 0..50 of triangle, flattened

Rows 0-49 are A000007, A000012, A000079, A000244, A000302, A000351, A000400, A000420, A001018, A001019, A011557, A001020, A001021, A001022, A001023, A001024, A001025, A001026, A001027, A001029, A009964-A009992, A087752.
Columns 0-26 are A000012, A001477, A000290, A000578, A000583, A000584, A001014, A001015, A001016, A001017, A008454, A008455, A008456, A010801-A010813, A089081.
Main diagonal is A000312. Other diagonals include A000169, A007778, A000272, A008788. Antidiagonal sums are in A026898.
Cf. A099555.
Transpose is A004248. See A051128, A095884, A009999 for other versions.
Cf. A277504 (unoriented), A293500 (chiral).

[[(n-k)^k: k in [0..n]]: n in [0..10]]; // G. C. Greubel, Nov 08 2018

Table[If[k == 0, 1, (n - k)^k], {n, 0, 11}, {k, 0, n}]//Flatten

T(n,k) = (n-k)^k \\ Charles R Greathouse IV, Feb 07 2017

E.g.f.: Sum T(n,k)*x^n*y^k/k! = 1/(1-x*exp(y)). - Paul D. Hanna, Oct 22 2004

E.g.f.: Sum T(n,k)*x^n/n!*y^k/k! = e^(x*e^y). - Franklin T. Adams-Watters, Jun 23 2006

More terms from David W. Wilson

Edited by Paul D. Hanna, Oct 22 2004

A089081 26th powers: a(n) = n^26.

Original entry on oeis.org

0, 1, 67108864, 2541865828329, 4503599627370496, 1490116119384765625, 170581728179578208256, 9387480337647754305649, 302231454903657293676544, 6461081889226673298932241, 100000000000000000000000000

Offset: 0

Douglas Winston (douglas.winston(AT)srupc.com), Dec 04 2003

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to divisibility sequences

Cf. A008454-A008456, A010801-A010813.

[n^26: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011

Range[0, 9]^26 (* Alonso del Arte, Apr 26 2015 *)

a(n)=n^26 \\ Charles R Greathouse IV, Jun 28 2015

a(n) = n^26.
Completely multiplicative sequence with a(p) = p^26 for prime p. Multiplicative sequence with a(p^e) = p^(26e). - Jaroslav Krizek, Nov 01 2009
From Amiram Eldar, Oct 09 2020: (Start)
Dirichlet g.f.: zeta(s-26).
Sum_{n>=1} 1/a(n) = zeta(26) = 1315862*Pi^26/11094481976030578125.
Sum_{n>=1} (-1)^(n+1)/a(n) = 33554431*zeta(26)/33554432 = 22076500342261*Pi^26/186134520519971831808000000. (End)

A122968 27th powers: a(n) = n^27.

Original entry on oeis.org

0, 1, 134217728, 7625597484987, 18014398509481984, 7450580596923828125, 1023490369077469249536, 65712362363534280139543, 2417851639229258349412352, 58149737003040059690390169

Offset: 0

Franklin T. Adams-Watters, Oct 27 2006

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A010812, A010813, A089081.

lst={}; Do[AppendTo[lst,n^27],{n,0,4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 15 2009 *)
Range[0,10]^27 (* Harvey P. Dale, Dec 17 2011 *)

Totally multiplicative sequence with a(p) = p^27 for prime p. Multiplicative sequence with a(p^e) = p^(27e). - Jaroslav Krizek, Nov 01 2009
From Amiram Eldar, Oct 09 2020: (Start)
Dirichlet g.f.: zeta(s-27).
Sum_{n>=1} 1/a(n) = zeta(27).
Sum_{n>=1} (-1)^(n+1)/a(n) = 67108863*zeta(27)/67108864. (End)

A122969 28th powers: a(n) = n^28.

Original entry on oeis.org

0, 1, 268435456, 22876792454961, 72057594037927936, 37252902984619140625, 6140942214464815497216, 459986536544739960976801, 19342813113834066795298816, 523347633027360537213511521

Offset: 0

Franklin T. Adams-Watters, Oct 27 2006

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A010813, A089081, A122968.

Table[n^28,{n,0,16}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2010 *)
Range[0,16]^28 (* Harvey P. Dale, Dec 09 2012 *)

Totally multiplicative sequence with a(p) = p^28 for prime p. Multiplicative sequence with a(p^e) = p^(28e). - Jaroslav Krizek, Nov 01 2009
From Amiram Eldar, Oct 09 2020: (Start)
Dirichlet g.f.: zeta(s-28).
Sum_{n>=1} 1/a(n) = zeta(28) = 6785560294*Pi^28/564653660170076273671875.
Sum_{n>=1} (-1)^(n+1)/a(n) = 134217727*zeta(28)/134217728 = 65053034220152267*Pi^28/5413323669636552217067520000000. (End)

A137489 Numbers with 26 divisors.

Original entry on oeis.org

12288, 20480, 28672, 45056, 53248, 69632, 77824, 94208, 118784, 126976, 151552, 167936, 176128, 192512, 217088, 241664, 249856, 274432, 290816, 299008, 323584, 339968, 364544, 397312, 413696, 421888, 438272, 446464, 462848, 520192, 536576

Offset: 1

R. J. Mathar, Apr 22 2008

nonn

Maple implementation: see A030513.

Numbers of the form p^25 (5th powers of A050997, subset of A010813) or p*q^12, where p and q are distinct primes. - R. J. Mathar, Mar 01 2010

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A030513-A030516, A030626, A030627, A030634-A030638, A005179, A003680, A096932, A061286, A061283.

Select[Range[900000],DivisorSigma[0,#]==26&] (* Vladimir Joseph Stephan Orlovsky, May 05 2011 *)

is(n)=numdiv(n)==26 \\ Charles R Greathouse IV, Jun 19 2016

A000005(a(n))=26.

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A248132 Integer part of square root of A010813(n) = n^25.

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A003992 Square array read by upwards antidiagonals: T(n,k) = n^k for n >= 0, k >= 0.

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A089081 26th powers: a(n) = n^26.

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A122968 27th powers: a(n) = n^27.

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A122969 28th powers: a(n) = n^28.

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A137489 Numbers with 26 divisors.

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