A008475 -id:A008475 - cp's OEIS frontend

A078779 Union of S, 2S and 4S, where S = odd squarefree numbers (A056911).

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 101

Offset: 1

Benoit Cloitre, Jan 11 2003

nonn

Numbers n such that the cyclic group Z_n is a DCI-group.
Numbers n such that A008475(n) = A001414(n).
A193551(a(n)) = A000026(a(n)) = a(n). - Reinhard Zumkeller, Aug 27 2011
Union of squarefree numbers and twice the squarefree numbers (A005117). - Reinhard Zumkeller, Feb 11 2012
The complement is A046790. - Omar E. Pol, Jun 11 2016

T. D. Noe, Table of n, a(n) for n = 1..7098
B. Alspach and M. Mishna, Enumeration of Cayley graphs and digraphs, Discr. Math., 256 (2002), 527-539.
M. Mishna, Home Page
M. Muzychuk, On Adam's conjecture for circulant graphs, Discr. Math. 167 (1997), 497-510.

Cf. A121176, A121684, A008475, A001414, A046790.

a078779 n = a078779_list !! (n-1)
a078779_list = m a005117_list $ map (* 2) a005117_list where
   m xs'@(x:xs) ys'@(y:ys) | x < y     = x : m xs ys'
                           | x == y    = x : m xs ys
                           | otherwise = y : m xs' ys
-- Reinhard Zumkeller, Feb 11 2012, Aug 27 2011

is(n)=issquarefree(n/gcd(n,2)) \\ Charles R Greathouse IV, Nov 05 2017

a(n) = (Pi^2/7)*n + O(sqrt(n)). - Vladimir Shevelev, Jun 08 2016

Edited by N. J. A. Sloane, Sep 13 2006

A222416 If n = Product (p_j^k_j) then a(n) = Sum (p_j^k_j) (a(1) = 1 by convention).

Original entry on oeis.org

1, 2, 3, 4, 5, 5, 7, 8, 9, 7, 11, 7, 13, 9, 8, 16, 17, 11, 19, 9, 10, 13, 23, 11, 25, 15, 27, 11, 29, 10, 31, 32, 14, 19, 12, 13, 37, 21, 16, 13, 41, 12, 43, 15, 14, 25, 47, 19, 49, 27, 20, 17, 53, 29, 16, 15, 22, 31, 59, 12, 61, 33, 16, 64, 18, 16, 67, 21, 26, 14, 71, 17, 73

Offset: 1

N. J. A. Sloane, Feb 28 2013

nonn

A variant of A008475, which is the main entry.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Nussbaum, Roger D.; Verduyn Lunel, Sjoerd M., Asymptotic estimates for the periods of periodic points of non-expansive maps, Ergodic Theory Dynam. Systems 23 (2003), no. 4, 1199--1226. See the function S(n). MR1997973 (2004m:37033)

Cf. A008475, A222415.

Array[Total[Power @@@ FactorInteger[#]] &, 73] (* Michael De Vlieger, Nov 17 2017 *)

A008475(n) = { my(f=factor(n)); vecsum(vector(#f~,i,f[i,1]^f[i,2])); };
A222416(n) = if(1==n,n,A008475(n)); \\ Antti Karttunen, Nov 17 2017

A051703 Maximal value of products of partitions of n into powers of distinct primes (1 not considered a power).

Original entry on oeis.org

1, 0, 2, 3, 4, 6, 0, 12, 15, 20, 30, 28, 60, 40, 84, 105, 140, 210, 180, 420, 280, 330, 360, 840, 504, 1260, 1155, 1540, 2310, 2520, 4620, 3080, 5460, 3960, 9240, 5544, 13860, 6552, 16380, 15015, 27720, 30030, 32760, 60060, 40040, 45045, 51480, 120120

Offset: 0

Vladeta Jovovic

nonn

			a(11) = 28 because max{11, 2*3^2, 2^3*3, 2^2*7} = 28.

Robert Gerbicz, Table of n, a(n) for n = 0..1000
J. Bamberg, G. Cairns and D. Kilminster, The crystallographic restriction, permutations and Goldbach's conjecture, Amer. Math. Monthly, 110 (March 2003), 202-209.

Largest element of n-th row of A080743.
A000793(n)=max{A000793(n-1), a(n)}, A000793(0)=1.
Cf. A008475, A051613, A080743, A080744, A051704.

b:= proc(n, i) option remember; local p;
      p:= `if`(i<1, 1, ithprime(i));
      `if`(n=0, 1, `if`(i<1 or n<0, 0, max(b(n, i-1),
      seq(p^j*b(n-p^j, i-1), j=1..ilog[p](n))) ))
    end:
a:= n-> b(n, numtheory[pi](n)):
seq(a(n), n=0..60);  # Alois P. Heinz, Feb 16 2013

nmax = 48; Do[a[n]=0, {n, 1, nmax}]; km = PrimePi[nmax]; For[k=1, k <= km, k++, q = 1; p = Prime[k]; For[i=nmax, i >= 1, i--, q=1; While[q*p <= i, q *= p; If[i == q, m = q, If[a[i - q] != 0, m = q*a[i - q], m = 0]]; a[i] = Max[a[i], m]]]]; a[0] = 1; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Aug 02 2012, translated from Robert Gerbicz's Pari program *)

{N=1000;v=vector(N,i,0);forprime(p=2,N,q=1;forstep(i=N,1,-1,
q=1;while(q*p<=i,q*=p;if(i==q,M=q,if(v[i-q],M=q*v[i-q],M=0));
v[i]=max(v[i],M))));print(0" "1);for(i=1,N,print(i" "v[i]))} \\ Robert Gerbicz, Jul 31 2012

Corrected and extended by Robert Gerbicz, Jul 31 2012

A082090 Length of iteration sequence if function A056239, a pseudo-logarithm is iterated and started at n. Fixed point equals zero for all initial values.

Original entry on oeis.org

2, 3, 4, 4, 5, 5, 5, 5, 5, 5, 6, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 6, 6, 6, 6, 6, 7, 6, 7, 6, 7, 6, 7, 7, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6, 6, 7, 6, 6, 7, 6, 6, 7, 7, 6, 7, 6, 7, 6, 6, 6, 7, 6, 7, 6, 6, 7

Offset: 1

Labos Elemer, Apr 09 2003

nonn

From Gus Wiseman, Dec 01 2023: (Start)
Conjecture:
- The position of first appearance of k is n = A007097(k-2).
- The position of last appearance of k is n = A014221(k-2) = 2^^(k-2).
- The number of times k appears is: 1, 1, 2, 8, 435, ...
(End)

			n=127:list={127,31,11,5,3,2,1,0},a[127]=8

Mohammad K. Azarian, On the Fixed Points of a Function and the Fixed Points of its Composite Functions, International Journal of Pure and Applied Mathematics, Vol. 46, No. 1, 2008, pp. 37-44. Mathematical Reviews, MR2433713 (2009c:65129), March 2009. Zentralblatt MATH, Zbl 1160.65015.
Mohammad K. Azarian, Fixed Points of a Quadratic Polynomial, Problem 841, College Mathematics Journal, Vol. 38, No. 1, January 2007, p. 60. Solution published in Vol. 39, No. 1, January 2008, pp. 66-67.

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Cf. A008475, A001414, A082083-A082086, A082091.
A112798 lists prime indices, length A001222, sum A056239.
A304038 lists distinct prime indices, length A001221, sum A066328.
Cf. A000079, A000720, A052410, A181819, A225485, A238747, A288636, A296150.

f:= n-> add (numtheory[pi](i[1])*i[2], i=ifactors(n)[2]):
a:= n-> 1+ `if`(n=1, 1, a(f(n))):
seq (a(n), n=1..120);  # Alois P. Heinz, Aug 09 2012

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] ep[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] bpi[x_] := Table[PrimePi[Part[ba[x], j]], {j, 1, lf[x]}] api[x_] := Apply[Plus, ep[x]*bpi[x]] Table[Length[FixedPointList[api, w]]-1, {w, 2, 128}]
Table[Length[FixedPointList[Total[PrimePi/@Join@@ ConstantArray@@@FactorInteger[#]]&,n]]-1, {n,100}] (* Gus Wiseman, Dec 01 2023 *)

A159685 Maximal product of distinct primes whose sum is <= n.

Original entry on oeis.org

1, 2, 3, 3, 6, 6, 10, 15, 15, 30, 30, 42, 42, 70, 105, 105, 210, 210, 210, 210, 330, 330, 462, 462, 770, 1155, 1155, 2310, 2310, 2730, 2730, 2730, 2730, 4290, 4290, 6006, 6006, 10010, 15015, 15015, 30030, 30030, 30030, 30030, 39270, 39270, 46410, 46410

Offset: 1

Wouter Meeussen, Apr 19 2009, May 02 2009

nonn

Equivalently, largest value of the LCM of the partitions of n into primes.
Equivalently, maximal number of times a permutation of length n, with prime cycle lengths, can operate on itself before returning to the initial permutation.
If the requirement that primes are distinct is dropped, this becomes A000792. - Charles R Greathouse IV, Jul 10 2012

			A permutation of length 10 can have prime cycle lengths of 2+3+5; so when repeatedly applied to itself, can produce at most 2*3*5 different permutations.
The products of distinct primes whose sum is <= 10 are 1 (the empty product), 2, 3, 5, 7, 2*3=6, 2*5=10, 2*7=14, 3*5=15, 3*7=21, and 2*3*5=30. The maximum is 30, so a(10) = 30. - _Jonathan Sondow_, Jul 06 2012

Alois P. Heinz, Table of n, a(n) for n = 1..10000
M. Deléglise and J.-L. Nicolas, Maximal product of primes whose sum is bounded, arXiv 1207.0603 [math.NT] (2012).
Marc Deléglise and Jean-Louis Nicolas, On the Largest Product of Primes with Bounded Sum, Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.8.
Marc Deléglise, Jean-Louis Nicolas, The Landau function and the Riemann hypothesis, Univ. Lyon (France, 2019).

Cf. A077011, A000793, A034891.

with(numtheory):
b:= proc(n,i) option remember; local p; p:= ithprime(max(i,1));
      `if`(n=0, 1, `if`(i<1, 0,
       max(b(n, i-1), `if`(p>n, 0, b(n-p, i-1)*p))))
    end:
a:= proc(n) option remember;
     `if`(n=0, 1, max(b(n, pi(n)), a(n-1)))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 04 2012

temp=Series[Times @@ (1/(1-q[ # ] x^#)& /@ Prepend[Prime /@ Range[24],1]),{x,0,Prime[24]}]; Table[Max[List @@ Expand[Coefficient[temp,x^n]]/. q[a_]^_ ->q[a] /.q->Identity],{n,64}]
(* Second program: *)
b[n_, i_] := b[n, i] = Module[{p = Prime[Max[i, 1]]}, If[n == 0, 1, If[i < 1, 0, Max[b[n, i-1], If[p > n, 0, b[n-p, i-1]*p]]]]]; a[n_] := a[n] = If[n == 0, 1, Max[b[n, PrimePi[n]], a[n-1]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Nov 05 2013, translated from Alois P. Heinz's Maple program *)

a(n) <= A002809(n) and A008475(a(n)) <= n (see (1.2) and (1.4) in Deléglise-Nicolas 2012). - Jonathan Sondow, Jul 04 2012.

A182938 If n = Product (p_j^e_j) then a(n) = Product (binomial(p_j, e_j)).

Original entry on oeis.org

1, 2, 3, 1, 5, 6, 7, 0, 3, 10, 11, 3, 13, 14, 15, 0, 17, 6, 19, 5, 21, 22, 23, 0, 10, 26, 1, 7, 29, 30, 31, 0, 33, 34, 35, 3, 37, 38, 39, 0, 41, 42, 43, 11, 15, 46, 47, 0, 21, 20, 51, 13, 53, 2, 55, 0, 57, 58, 59, 15, 61, 62, 21, 0, 65, 66

Offset: 1

Peter Luschny, Jan 16 2011

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Plot of Sum_{k=1..n} a(k) / n^2 for n = 1..1000000

Cf. A000026, A001414, A008473, A008474, A008475, A008476, A008477, A028310, A069799.

Cf. A027748, A124010, A007318, A328745.

a182938 n = product $ zipWith a007318'
   (a027748_row n) (map toInteger $ a124010_row n)
-- Reinhard Zumkeller, Feb 18 2012

A182938 := proc(n) local e,j; e := ifactors(n)[2]:
mul (binomial(e[j][1], e[j][2]), j=1..nops(e)) end:
seq (A182938(n), n=1..100);

a[n_] := Times @@ (Map[Binomial @@ # &, FactorInteger[n], 1]);
Table[a[n], {n, 1, 100}] (* Kellen Myers, Jan 16 2011 *)

a(n)=prod(i=1,#n=factor(n)~,binomial(n[1,i],n[2,i])) \\ M. F. Hasler

for(n=1, 100, print1(direuler(p=2, n, (1 + X)^p)[n], ", ")) \\ Vaclav Kotesovec, Mar 28 2025

a(A185359(n)) = 0. - Reinhard Zumkeller, Feb 18 2012
Dirichlet g.f.: Product_{p prime} (1 + p^(-s))^p. - Ilya Gutkovskiy, Oct 26 2019
Conjecture: Sum_{k=1..n} a(k) ~ c * n^2, where c = 0.33754... - Vaclav Kotesovec, Mar 28 2025

Given terms checked with new PARI code by M. F. Hasler, Jan 16 2011

A080743 Array read by rows in which n-th row lists orders of elements of Symm(n) that are not orders of elements of Symm(n-1) (6th row is empty, written as 0 by convention).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 0, 7, 10, 12, 8, 15, 9, 14, 20, 21, 30, 11, 18, 24, 28, 35, 42, 60, 13, 22, 36, 40, 33, 45, 70, 84, 26, 44, 56, 105, 16, 39, 55, 63, 66, 90, 120, 140, 17, 52, 72, 210, 65, 77, 78, 110, 126, 132, 168, 180, 19, 34, 48, 88, 165, 420, 51, 91, 99, 130, 154, 156, 220

Offset: 1

N. J. A. Sloane, Mar 08 2003

A051613 gives number of elements in n-th row.

			1;
2;
3;
4;
5, 6;
0;
7, 10, 12;
8, 15;
...

Alois P. Heinz, Rows n = 1..100, flattened
J. Bamberg, G. Cairns and D. Kilminster, The crystallographic restriction, permutations and Goldbach's conjecture, Amer. Math. Monthly, 110 (March 2003), 202-209.

Cf. A008475, A051613, A080744, A051703.

b:= proc(n) option remember; `if`(n<3, {n},
      {n, seq(map(x-> ilcm(x, i), b(n-i))[], i=2..n-1)}
       minus {seq(b(i)[], i=1..n-1)})
    end:
T:= proc(n) local l; l:= [b(n, n)[]];
      `if`(nops(l)=0, 0, sort(l)[])
    end:
seq(T(n), n=1..20);  # Alois P. Heinz, Feb 15 2013

b[n_, i_] := b[n, i] = Module[{p}, p = If[i<1, 1, Prime[i]]; If[n == 0, 1, If[i<1 || n<0, 0, Max[Join[{b[n, i-1]}, Table[p^j*b[n-p^j, i-1], {j, 1, Log[p, n]}]]]]] ]; T[1] = {1}; T[6] = {0}; T[n_] := Reap[For[m = n, m <= b[n, PrimePi[n]], m++,  If[n == Total[Power @@@ FactorInteger[m]], Sow[m]]]][[2, 1]]; Table[T[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Feb 26 2015, after Alois P. Heinz *)

n-th row = set of m such that A008475(m) = n, or 0 if no such m exists.

More terms from Vladeta Jovovic, Mar 12 2003

A304037 If n = Product (p_j^k_j) then a(n) = Sum (pi(p_j)^k_j), where pi() = A000720.

Original entry on oeis.org

0, 1, 2, 1, 3, 3, 4, 1, 4, 4, 5, 3, 6, 5, 5, 1, 7, 5, 8, 4, 6, 6, 9, 3, 9, 7, 8, 5, 10, 6, 11, 1, 7, 8, 7, 5, 12, 9, 8, 4, 13, 7, 14, 6, 7, 10, 15, 3, 16, 10, 9, 7, 16, 9, 8, 5, 10, 11, 17, 6, 18, 12, 8, 1, 9, 8, 19, 8, 11, 8, 20, 5, 21, 13, 11, 9, 9, 9, 22, 4, 16, 14, 23, 7, 10, 15, 12, 6

Offset: 1

Ilya Gutkovskiy, May 05 2018

nonn

			a(72) = 5 because 72 = 2^3*3^2 = prime(1)^3*prime(2)^2 and 1^3 + 2^2 = 5.

Ilya Gutkovskiy, Extended graphical example
Index entries for sequences computed from indices in prime factorization

Cf. A000040, A000720, A002110, A003963, A008475, A056239, A066328, A156061, A222416.

a[n_] := Plus @@ (PrimePi[#[[1]]]^#[[2]]& /@ FactorInteger[n]); a[1] = 0; Table[a[n], {n, 1, 88}]

If gcd(u,v) = 1 then a(u*v) = a(u) + a(v).
a(p^k) = A000720(p)^k where p is a prime.
a(A002110(m)^k) = 1^k + 2^k + ... + m^k.
As an example:
a(A000040(k)) = k.
a(A006450(k)) = A000040(k).
a(A038580(k)) = A006450(k).
a(A001248(k)) = a(A011757(k)) = A000290(k).
a(A030078(k)) = a(A055875(k)) = A000578(k).
a(A002110(k)) = a(A011756(k)) = A000217(k).
a(A061742(k)) = A000330(k).
a(A115964(k)) = A000537(k).
a(A080696(k)) = A007504(k).
a(A076954(k)) = A001923(k).

A304251 If n = Product (p_j^k_j) then a(n) = Sum (prime(p_j)^k_j).

Original entry on oeis.org

0, 3, 5, 9, 11, 8, 17, 27, 25, 14, 31, 14, 41, 20, 16, 81, 59, 28, 67, 20, 22, 34, 83, 32, 121, 44, 125, 26, 109, 19, 127, 243, 36, 62, 28, 34, 157, 70, 46, 38, 179, 25, 191, 40, 36, 86, 211, 86, 289, 124, 64, 50, 241, 128, 42, 44, 72, 112, 277, 25, 283, 130, 42, 729, 52, 39, 331, 68, 88, 31

Offset: 1

Ilya Gutkovskiy, May 09 2018

nonn

			a(12) = 14 because 12 = 2^2*3 and prime(2)^2 + prime(3) = 3^2 + 5 = 14.

Robert Israel, Table of n, a(n) for n = 1..10000
Ilya Gutkovskiy, Scatter plot of a(n) up to n=100000
Index entries for sequences computed from indices in prime factorization

Cf. A000040, A002110, A006450, A008475, A038580, A064988, A083186, A222416, A304037, A304253 (fixed points).

f:= proc(n) local t;
   add(ithprime(t[1])^t[2],t=ifactors(n)[2])
end proc:
map(f, [$1..100]); # Robert Israel, Apr 25 2024

a[n_] := Plus @@ (Prime[#[[1]]]^#[[2]] & /@ FactorInteger[n]); a[1] = 0; Table[a[n], {n, 70}]

a(n) = my(f=factor(n)); sum(k=1, #f~, prime(f[k,1])^f[k,2]); \\ Michel Marcus, May 09 2018

a(prime(i)^k) = prime(prime(i))^k.
a(A000040(k)) = A006450(k).
a(A006450(k)) = A038580(k).
a(A002110(k)) = A083186(k).

A340901 Additive with a(p^e) = (-p)^e.

Original entry on oeis.org

0, -2, -3, 4, -5, -5, -7, -8, 9, -7, -11, 1, -13, -9, -8, 16, -17, 7, -19, -1, -10, -13, -23, -11, 25, -15, -27, -3, -29, -10, -31, -32, -14, -19, -12, 13, -37, -21, -16, -13, -41, -12, -43, -7, 4, -25, -47, 13, 49, 23, -20, -9, -53, -29, -16, -15, -22, -31

Offset: 1

Sebastian Karlsson, Jan 26 2021

The sequence contains every integer infinitely many times.
Proof (outline):
1. Every integer m > 9 is the sum of distinct odd primes [R. E. Dressler].
2. Any integer k (positive as negative) can be written as k = 4^e - m, for sufficiently large and infinitely many e > 0 and m > 9.
3. Pick an arbitrary integer k and write it like k = 4^e - m. Let p_1, p_2, ..., p_i be distinct odd primes such that p_1 + p_2 + ... + p_i = m. Then a(p_1*p_2*...*p_i*4^e) = 4^e - m = k. Since there are infinitely many representations of any k of the form 4^e - m, this means that there are infinitely many n such that a(n) = k.
Q.E.D.

			a(20) = a(2^2*5) = (-2)^2 + (-5) = -1.

Sebastian Karlsson, Table of n, a(n) for n = 1..10000
R. E. Dressler, A stronger Bertrand's postulate with an application to partitions, Proc. Amer. Math. Soc., 33 (1972), 226-228.

Cf. A001414, A002035, A008472, A008475, A008476, A316523.

⍝ Dyalog dialect
A340901 ← {1=⍵:0 ⋄ +/{(-⍺)*≢⍵}⌸factors(⍵)} ⍝ Needs also factors function from https://dfns.dyalog.com/c_factors.htm - Antti Karttunen, Feb 16 2024

a[n_] := Total@ (((-First[#])^Last[#]) & /@ FactorInteger[n]); a[1] = 0; Array[a, 100] (* Amiram Eldar, May 15 2023 *)

a(n) = my(f=factor(n)); sum(k=1, #f~, (-f[k,1])^f[k,2]); \\ Michel Marcus, Jan 26 2021

from sympy import primefactors as pf, multiplicity as mult
def a(n):
    return sum([(-p)**mult(p, n) for p in pf(n)])
for n in range(1, 59):
    print(a(n), end=', ')

a(A002035(n)) = - A008475(A002035(n)).

a(n^2) = A008475(n^2).

cp's OEIS Frontend

A078779 Union of S, 2S and 4S, where S = odd squarefree numbers (A056911).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

PARI

Formula

Extensions

A222416 If n = Product (p_j^k_j) then a(n) = Sum (p_j^k_j) (a(1) = 1 by convention).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

A051703 Maximal value of products of partitions of n into powers of distinct primes (1 not considered a power).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions

A082090 Length of iteration sequence if function A056239, a pseudo-logarithm is iterated and started at n. Fixed point equals zero for all initial values.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Maple

Mathematica

A159685 Maximal product of distinct primes whose sum is <= n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A182938 If n = Product (p_j^e_j) then a(n) = Product (binomial(p_j, e_j)).

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

PARI

Formula

Extensions

A080743 Array read by rows in which n-th row lists orders of elements of Symm(n) that are not orders of elements of Symm(n-1) (6th row is empty, written as 0 by convention).

Views

Author

Keywords

Comments

Examples

Links