A009967 -id:A009967 - cp's OEIS frontend

A147641 Numbers B in the triples (A,B,C) that set a record in the L-function of the ABC conjecture if the search for C admits only the restricted integer subset of A009967 as described in A147642.

Original entry on oeis.org

16, 512, 12005, 6436341

Offset: 1

Artur Jasinski, Nov 09 2008

If the ABC conjecture is true this sequence is finite.

For numbers A for this case see A147643.

OEIS Index entries for sequences related to the abc conjecture.

Cf. A085152, A085153, A147298 - A147307, A147638 - A147643.

A008472 Sum of the distinct primes dividing n.

Original entry on oeis.org

0, 2, 3, 2, 5, 5, 7, 2, 3, 7, 11, 5, 13, 9, 8, 2, 17, 5, 19, 7, 10, 13, 23, 5, 5, 15, 3, 9, 29, 10, 31, 2, 14, 19, 12, 5, 37, 21, 16, 7, 41, 12, 43, 13, 8, 25, 47, 5, 7, 7, 20, 15, 53, 5, 16, 9, 22, 31, 59, 10, 61, 33, 10, 2, 18, 16, 67, 19, 26, 14, 71, 5, 73

Offset: 1

Olivier Gérard

Sometimes called sopf(n).
Sum of primes dividing n (without repetition) (compare A001414).
Equals A051731 * A061397 = inverse Mobius transform of [0, 2, 3, 0, 5, 0, 7, ...]. - Gary W. Adamson, Feb 14 2008
Equals row sums of triangle A143535. - Gary W. Adamson, Aug 23 2008
a(n) = n if and only if n is prime. - Daniel Forgues, Mar 24 2009
a(n) = n is a new record if and only if n is prime. - Zak Seidov, Jun 27 2009
a(A001043(n)) = A191583(n);
For n > 0: a(A000079(n)) = 2, a(A000244(n)) = 3, a(A000351(n)) = 5, a(A000420(n)) = 7;
a(A006899(n)) <= 3; a(A003586(n)) = 5; a(A033846(n)) = 7; a(A033849(n)) = 8; a(A033847(n)) = 9; a(A033850(n)) = 10; a(A143207(n)) = 10. - Reinhard Zumkeller, Jun 28 2011
For n > 1: a(n) = Sum(A027748(n,k): 1 <= k <= A001221(n)). - Reinhard Zumkeller, Aug 27 2011
If n is the product of twin primes (A037074), a(n) = 2*sqrt(n+1) = sqrt(4n+4). - Wesley Ivan Hurt, Sep 07 2013
From Wilf A. Wilson, Jul 21 2017: (Start)
a(n) + 2, n > 2, is the number of maximal subsemigroups of the monoid of orientation-preserving or -reversing mappings on a set with n elements.
a(n) + 3, n > 2, is the number of maximal subsemigroups of the monoid of orientation-preserving or -reversing partial mappings on a set with n elements.
(End)
The smallest m such that a(m) = n, or 0 if no such number m exists is A064502(n). The only integers that are not in the sequence are 1, 4 and 6. - Bernard Schott, Feb 07 2022

			a(18) = 5 because 18 = 2 * 3^2 and 2 + 3 = 5.
a(19) = 19 because 19 is prime.
a(20) = 7 because 20 = 2^2 * 5 and 2 + 5 = 7.

Daniel Forgues, Table of n, a(n) for n = 1..100000 (first 10000 terms from Franklin T. Adams-Watters)
Johann Bartel, R. K. Bhaduri, Matthias Brack, and M. V. N. Murthy, On the asymptotic prime partitions of integers, arXiv:1609.06497 [math-ph], 2017.
James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017. [_Wilf A. Wilson_, Jul 21 2017]

First difference of A024924.
Cf. A001414 (sopfr), A001222, A051731, A061397, A064502, A085020, A143535.
Sum of the k-th powers of the primes dividing n for k=0..10 : A001221 (k=0), this sequence (k=1), A005063 (k=2), A005064 (k=3), A005065 (k=4), A351193 (k=5), A351194 (k=6), A351195 (k=7), this sequence (k=8), A351197 (k=9), A351198 (k=10).
Cf. A010051.

a008472 = sum . a027748_row  -- Reinhard Zumkeller, Mar 29 2012

[n eq 1 select 0 else &+[p[1]: p in Factorization(n)]: n in [1..100]]; // Vincenzo Librandi, Jun 24 2017

A008472 := n -> add(d, d = select(isprime, numtheory[divisors](n))):
seq(A008472(i), i = 1..40); # Peter Luschny, Jan 31 2012
A008472 := proc(n)
        add( d, d= numtheory[factorset](n)) ;
end proc: # R. J. Mathar, Jul 08 2012

Prepend[Array[Plus @@ First[Transpose[FactorInteger[#]]] &, 100, 2], 0]
Join[{0}, Rest[Total[Transpose[FactorInteger[#]][[1]]]&/@Range[100]]] (* Harvey P. Dale, Jun 18 2012 *)
(* Requires version 7.0+ *) Table[DivisorSum[n, # &, PrimeQ[#] &], {n, 75}] (* Alonso del Arte, Dec 13 2014 *)
Table[Sum[p, {p, Select[Divisors[n], PrimeQ]}], {n, 1, 100}] (* Vaclav Kotesovec, May 20 2020 *)

sopf(n) = local(fac=factor(n)); sum(i=1,matsize(fac)[1],fac[i,1])

vector(100,n,vecsum(factor(n)[,1]~)) \\ Derek Orr, May 13 2015

A008472(n)=vecsum(factor(n)[,1]) \\ M. F. Hasler, Jul 18 2015

from sympy import primefactors
def A008472(n): return sum(primefactors(n)) # Chai Wah Wu, Feb 03 2022

def A008472(n):
    return add(d for d in divisors(n) if is_prime(d))
print([A008472(i) for i in (1..40)]) # Peter Luschny, Jan 31 2012

[sum(prime_factors(n)) for n in range(1,74)] # Giuseppe Coppoletta, Jan 19 2015

Let n = Product_j prime(j)^k(j) where k(j) >= 1, then a(n) = Sum_j prime(j).
Additive with a(p^e) = p.
G.f.: Sum_{k >= 1} prime(k)*x^prime(k)/(1-x^prime(k)). - Franklin T. Adams-Watters, Sep 01 2009
L.g.f.: -log(Product_{k>=1} (1 - x^prime(k))) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 06 2017
Dirichlet g.f.: primezeta(s-1)*zeta(s). - Benedict W. J. Irwin, Jul 11 2018
a(n) = Sum_{p|n, p prime} p. - Wesley Ivan Hurt, Feb 04 2022
From Bernard Schott, Feb 07 2022: (Start)
For n > 0: a(A001020(n)) = 11, a(A001022(n)) = 13, a(A001026(n)) = 17, a(A001029(n)) = 19, a(A009967(n)) = 23, a(A009973(n)) = 29, a(A009975(n)) = 31, a(A009981(n)) = 37, a(A009985(n)) = 41, a(A009987(n)) = 43, a(A009991(n)) = 47.
For p odd prime, a(2*p) = p+2 <==> a(A100484(n)) = A052147(n) for n > 1. (End)
a(n) = Sum_{d|n} d * c(d), where c = A010051. - Wesley Ivan Hurt, Jun 22 2024

A153656 Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + (2j +3)prime(j)*T(n-2, k-1) with j=9, read by rows.

Original entry on oeis.org

2, 23, 23, 2, 1054, 2, 2, 12165, 12165, 2, 2, 13133, 533412, 13133, 2, 2, 14101, 6422240, 6422240, 14101, 2, 2, 15069, 12779580, 270482476, 12779580, 15069, 2, 2, 16037, 19605432, 3385203976, 3385203976, 19605432, 16037, 2, 2, 17005, 26899796, 9577346548, 137413443860, 9577346548, 26899796, 17005, 2

Offset: 1

Roger L. Bagula, Dec 30 2008

			Triangle begins as:
   2;
  23,    23;
   2,  1054,        2;
   2, 12165,    12165,          2;
   2, 13133,   533412,      13133,            2;
   2, 14101,  6422240,    6422240,        14101,          2;
   2, 15069, 12779580,  270482476,     12779580,      15069,        2;
   2, 16037, 19605432, 3385203976,   3385203976,   19605432,    16037,     2;
   2, 17005, 26899796, 9577346548, 137413443860, 9577346548, 26899796, 17005, 2;

G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Sequences with variable (p,q,j): A153516 (0,1,2), A153518 (0,1,3), A153520 (0,1,4), A153521 (0,1,5), A153648 (1,0,3), A153649 (1,1,4), A153650 (1,4,5), A153651 (1,5,6), A153652 (2,1,7), A153653 (2,1,8), A153654 (2,1,9), A153655 (2,1,10), this sequence (2,3,9), A153657 (2,7,10).

Cf. A009967 (powers of 23).

f:= func< n,j | Round(((3-(-1)^n)/2)*NthPrime(j)^(n-1) - 2^((3-(-1)^n)/2)) >;
function T(n,k,p,q,j)
  if n eq 2 then return NthPrime(j);
  elif (n eq 3 and k eq 2 or n eq 4 and k eq 2 or n eq 4 and k eq 3) then return f(n,j);
  elif (k eq 1 or k eq n) then return 2;
  else return T(n-1,k,p,q,j) + T(n-1,k-1,p,q,j) + (p*j+q)*NthPrime(j)*T(n-2,k-1,p,q,j);
  end if; return T;
end function;
[T(n,k,2,3,9): k in [1..n], n in [1..12]]; // G. C. Greubel, Mar 06 2021

T[n_, k_, p_, q_, j_]:= T[n,k,p,q,j]= If[n==2, Prime[j], If[n==3 && k==2 || n==4 && 2<=k<=3, ((3-(-1)^n)/2)*Prime[j]^(n-1) -2^((3-(-1)^n)/2), If[k==1 || k==n, 2, T[n-1,k,p,q,j] + T[n-1,k-1,p,q,j] + (p*j+q)*Prime[j]*T[n-2,k-1,p,q,j] ]]];
Table[T[n,k,2,3,9], {n,12}, {k,n}]//Flatten (* modified by G. C. Greubel, Mar 06 2021 *)

@CachedFunction
def f(n,j): return ((3-(-1)^n)/2)*nth_prime(j)^(n-1) - 2^((3-(-1)^n)/2)
def T(n,k,p,q,j):
    if (n==2): return nth_prime(j)
    elif (n==3 and k==2 or n==4 and 2<=k<=3): return f(n,j)
    elif (k==1 or k==n): return 2
    else: return T(n-1,k,p,q,j) + T(n-1,k-1,p,q,j) + (p*j+q)*nth_prime(j)*T(n-2,k-1,p,q,j)
flatten([[T(n,k,2,3,9) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Mar 06 2021

T(n, k) = T(n-1, k) + T(n-1, k-1) + (2*j +3)*prime(j)*T(n-2, k-1) with j=9.
From G. C. Greubel, Mar 06 2021: (Start)
T(n,k,p,q,j) = T(n-1,k,p,q,j) + T(n-1,k-1,p,q,j) + (p*j+q)*prime(j)*T(n-2,k-1,p,q,j) with T(2,k,p,q,j) = prime(j), T(3,2,p,q,j) = 2*prime(j)^2 -4, T(4,2,p,q,j) = T(4,3,p,q,j) = prime(j)^2 -2, T(n,1,p,q,j) = T(n,n,p,q,j) = 2 and (p,q,j) = (2,3,9).
Sum_{k=0..n} T(n,k,p,q,j) = 2*prime(j)^(n-1), for (p,q,j)=(2,3,9), = 2*A009967(n-1). (End)

Edited by G. C. Greubel, Mar 06 2021

A319075 Square array T(n,k) read by antidiagonal upwards in which row n lists the n-th powers of primes, hence column k lists the powers of the k-th prime, n >= 0, k >= 1.

Original entry on oeis.org

1, 2, 1, 4, 3, 1, 8, 9, 5, 1, 16, 27, 25, 7, 1, 32, 81, 125, 49, 11, 1, 64, 243, 625, 343, 121, 13, 1, 128, 729, 3125, 2401, 1331, 169, 17, 1, 256, 2187, 15625, 16807, 14641, 2197, 289, 19, 1, 512, 6561, 78125, 117649, 161051, 28561, 4913, 361, 23, 1, 1024, 19683, 390625, 823543, 1771561, 371293

Offset: 0

Omar E. Pol, Sep 09 2018

If n = p - 1 where p is prime, then row n lists the numbers with p divisors.

The partial sums of column k give the column k of A319076.

			The corner of the square array is as follows:
         A000079 A000244 A000351  A000420    A001020    A001022     A001026
A000012        1,      1,      1,       1,         1,         1,          1, ...
A000040        2,      3,      5,       7,        11,        13,         17, ...
A001248        4,      9,     25,      49,       121,       169,        289, ...
A030078        8,     27,    125,     343,      1331,      2197,       4913, ...
A030514       16,     81,    625,    2401,     14641,     28561,      83521, ...
A050997       32,    243,   3125,   16807,    161051,    371293,    1419857, ...
A030516       64,    729,  15625,  117649,   1771561,   4826809,   24137569, ...
A092759      128,   2187,  78125,  823543,  19487171,  62748517,  410338673, ...
A179645      256,   6561, 390625, 5764801, 214358881, 815730721, 6975757441, ...
...

Rows 0-13: A000012, A000040, A001248, A030078, A030514, A050997, A030516, A092759, A179645, A179665, A030629, A079395, A030631, A138031.
Other rows n: A030635 (n=16), A030637 (n=18), A137486 (n=22), A137492 (n=28), A139571 (n=30), A139572 (n=36), A139573 (n=40), A139574 (n=42), A139575 (n=46), A173533 (n=52), A183062 (n=58), A183085 (n=60), A261700 (n=100).
Columns 1-15: A000079, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991.
Main diagonal gives A093360.
Second diagonal gives A062457.
Third diagonal gives A197987.
Removing the 1's we have A182944/ A182945.
Cf. A006093, A319074, A319076.

PARI
```
T(n, k) = prime(k)^n;
```

T(n,k) = A000040(k)^n, n >= 0, k >= 1.

A073215 Sum of two powers of 23.

Original entry on oeis.org

2, 24, 46, 530, 552, 1058, 12168, 12190, 12696, 24334, 279842, 279864, 280370, 292008, 559682, 6436344, 6436366, 6436872, 6448510, 6716184, 12872686, 148035890, 148035912, 148036418, 148048056, 148315730, 154472232, 296071778

Offset: 0

Jeremy Gardiner, Jul 20 2002

			T(2,0) = 23^2 + 23^0 = 530.
Table begins:
       2;
      24,     46;
     530,    552,   1058;
   12168,  12190,  12696,  24334;
  279842, 279864, 280370, 292008, 559682;
  ...

G. C. Greubel, Table of n, a(n) for n = 0..999 [Offset changed to 0 by _Georg Fischer_, Mar 01 2022]

Cf. A009967.
Equals twice A072822.
Sums of two powers of n: A073423 (0), A007395 (1), A173786 (2), A055235 (3), A055236 (4), A055237 (5), A055257 (6), A055258 (7), A055259 (8), A055260 (9), A052216 (10), A073211 (11), A194887 (12), A072390 (13), A055261 (16), A073213 (17), A073214 (19).

With[{nn=30},Take[Union[Total/@Tuples[23^Range[0,nn],2]],nn]] (* Harvey P. Dale, Oct 16 2017 *)

from math import isqrt
def A073215(n): return 23**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+23**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 09 2025

T(n, m) = 23^n + 23^m, for n >= 0 and m in [0..n].

Bivariate g.f.: (2 - 24*x) / ((1 - x) * (1 - 23*x) * (1 - 23*x*y)). - J. Douglas Morrison, Jul 29 2021

A147642 Numbers C which generate successive records of the merit function of the ABC conjecture admitting only C which are powers of 23.

Original entry on oeis.org

23, 529, 12167, 6436343

Offset: 1

Artur Jasinski, Nov 09 2008

In a variant of the ABC conjecture (see A120498) we look at triples (A,B,C) restricted to A+B=C, gcd(A,B)=1, and at the merit function L(A,B,C)=log(C)/log(rad(A*B*C)), where rad() is the squarefree kernel A007947, as usual. Watching for records in L() as C runs through the integers generates A147302. In this sequence here, we admit only the C of the form 23^x, see A009967, which avoids some early larger records that would be created by unrestricted C, and leads to a slower increase of the L-values.

For associated B for this case see A147641, for associated A see A147643.

			C= 23 is the first candidate (and therefore by definition a record). Scanning the pairs (A,B) for this C we have L-values of L(1,22,23) = 0.5035, L(2,21,23) = 0.456, ... L(6,17,23) = 0.404, L(7,16,23) = 0.542 ,... L(11,12,23) = 0.428. The largest L-value stems from (A=7,B=16) which means the representative triple of the first record is (A,B,C) = (7,16,23).
C= 23^2= 529 is the next candidate. Scanning again all (A,B) values subject to the constraints we achieve L(17,512,529) = 0.941... (Smaller ones like L(81,448,529) = 0.9123... are discarded). Since the L-value for C=529 is larger than the L-value for C=23, the next record is C=529 with representatives (A,B,C)= (17,512,529).
The third candidate is C= 23^3= 12167. This generates a maximum of L(162,12005,12167) = 1.1089... (smaller values like L(17,12150,12167) = 1.0039.. discarded) which is again larger than the maximum of the previous record (which was 0.941..) So the C-value of 12167 is again a record-holder.

OEIS Index entries for sequences related to the abc conjecture.

Cf. A085152, A085153, A147298 - A147307, A147638 - A147643.

A159858 Numerator of Hermite(n, 1/23).

Original entry on oeis.org

1, 2, -1054, -6340, 3332716, 33496312, -17563075016, -247760738608, 129576612091280, 2356200115760672, -1229116100101646816, -27386829424951203392, 14249679514133063237824, 376202545407446604740480, -195237686946571258563550336, -5962787476468241626543090432

Offset: 0

N. J. A. Sloane, Nov 12 2009

Consider any odd integer k. B(n) = k^n Hermite(n,1/k) satisfies the recurrence B(n) = 2*B(n-1) - 2*k^2*(n-1)*B(n-2) with B(0) = 1 and B(1) = 2. In particular, B(n) == 2*B(n-1) mod k, and B(n) is coprime to k. Therefore B(n) is the numerator of Hermite(n,1/k). - Robert Israel, Jun 27 2014

			Numerator of 1, 2/23, -1054/529, -6340/12167, 3332716/279841, 33496312/6436343, -17563075016/148035889, -247760738608/3404825447, 129576612091280/78310985281...

G. C. Greubel, Table of n, a(n) for n = 0..385
DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Cf. A009967 (denominators).

[Numerator((&+[(-1)^k*Factorial(n)*(2/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

A159858 := proc(n)
        orthopoly[H](n,1/23) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Numerator[Table[HermiteH[n, 1/23], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)

a(n)=numerator(polhermite(n,1/23)) \\ Charles R Greathouse IV, Jan 29 2016

D-finite with recurrence a(n) - 2*a(n-1) + 1058*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
a(n) = 23^n * Hermite(n,1/23). This does satisfy the above formula. - Robert Israel, Jun 27 2014
From G. C. Greubel, Jun 09 2018: (Start)
E.g.f.: exp(2*x-529*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

A009990 Powers of 46.

Original entry on oeis.org

1, 46, 2116, 97336, 4477456, 205962976, 9474296896, 435817657216, 20047612231936, 922190162669056, 42420747482776576, 1951354384207722496, 89762301673555234816, 4129065876983540801536, 189937030341242876870656, 8737103395697172336050176, 401906756202069927458308096

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 46), L(1, 46), P(1, 46), T(1, 46). Essentially same as Pisot sequences E(46, 2116), L(46, 2116), P(46, 2116), T(46, 2116). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 46-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

T. D. Noe, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (46).

Cf. A000079, A008776, A009967.

[46^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010

46^Range[0,20] (* or *) NestList[46#&,1,20] (* Harvey P. Dale, Jan 15 2017 *)

G.f.: 1/(1-46*x). - Philippe Deléham, Nov 24 2008
a(n) = 46^n; a(n) = 46*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010
From Elmo R. Oliveira, Jul 10 2025: (Start)
E.g.f.: exp(46*x).
a(n) = A000079(n)*A009967(n). (End)

A180732 23^a(n) is smallest power of 23 beginning with n.

Original entry on oeis.org

0, 1, 7, 10, 2, 5, 8, 33, 11, 36, 14, 3, 28, 6, 42, 31, 20, 9, 34, 23, 12, 106, 1, 37, 26, 15, 4, 51, 40, 29, 123, 18, 347, 7, 43, 137, 32, 220, 21, 256, 10, 245, 46, 234, 35, 129, 505, 24, 400, 13, 248, 2, 49, 378, 38, 179, 461, 27, 215, 497, 16, 204, 486, 5, 193, 475, 41, 135

Offset: 1

Daniel Mondot, Sep 18 2010

Daniel Mondot, Table of n, a(n) for n = 1..32699

Cf. A009967, A180730, A180731.

A382535 Consecutive states of Lehmer's original linear congruential pseudo-random number generator 23*s mod (10^8+1) when started at s=1.

Original entry on oeis.org

1, 23, 529, 12167, 279841, 6436343, 48035888, 4825413, 10984498, 52643452, 10799384, 48385830, 12874079, 96103815, 10387723, 38917627, 95105413, 87424478, 10762974, 47548400, 93613190, 53103349, 21377015, 91671341, 8440822, 94138905, 65194794, 99480248

Offset: 1

Sean A. Irvine, May 25 2025

Periodic with period 5882352.

This is the first linear congruential pseudo-random number generator described in the literature. As such, it is the forerunner of one of the most widely used techniques for generating pseudo-random numbers.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
D. H. Lehmer, Mathematical methods in large-scale computing units, Proceedings of a Second Symposium on Large-Scale Digital Calculating Machinery (1949), 141-146.
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.

Cf. A009967.

Cf. A096550-A096561 (other pseudo-random number generators).

NestList[Mod[23*#, 10^8 + 1] &, 1, 50] (* Paolo Xausa, May 26 2025 *)

a(n) = 23 * a(n-1) mod (10^8+1).

cp's OEIS Frontend

A147641 Numbers B in the triples (A,B,C) that set a record in the L-function of the ABC conjecture if the search for C admits only the restricted integer subset of A009967 as described in A147642.

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A008472 Sum of the distinct primes dividing n.

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Magma

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PARI

PARI

PARI

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Sage

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A153656 Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + (2*j +3)*prime(j)*T(n-2, k-1) with j=9, read by rows.

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A319075 Square array T(n,k) read by antidiagonal upwards in which row n lists the n-th powers of primes, hence column k lists the powers of the k-th prime, n >= 0, k >= 1.

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PARI

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A073215 Sum of two powers of 23.

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Mathematica

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A147642 Numbers C which generate successive records of the merit function of the ABC conjecture admitting only C which are powers of 23.

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A159858 Numerator of Hermite(n, 1/23).

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Magma

A153656 Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + (2j +3)prime(j)*T(n-2, k-1) with j=9, read by rows.