A080497 -id:A080497 - cp's OEIS frontend

A072513 Product of all n - d, where d < n and d is a divisor of n.

1, 1, 2, 6, 4, 60, 6, 168, 48, 360, 10, 47520, 12, 1092, 1680, 20160, 16, 440640, 18, 820800, 5040, 4620, 22, 734469120, 480, 7800, 11232, 4953312, 28, 3946320000, 30, 9999360, 21120, 17952, 28560, 439723468800, 36, 25308, 35568, 35852544000

Offset: 1

Amarnath Murthy, Jul 28 2002

nonn

			a(6) = (6-1)(6-2)(6-3) = 60.
For n = 16 the divisors d < n are 1,2,4 and 8, so a(16) = (16-1)*(16-2)*(16-4)*(16-8) = 15*14*12*8 = 20160.

Ivan Neretin, Table of n, a(n) for n = 1..1000

Cf. A072512, A080497, A080498, A080500 (similar products), A258324 (LCM instead of product).

Cf. A027751.

a072513 n = product $ map (n -) $ a027751_row n
-- Reinhard Zumkeller, May 27 2015

Table[Times @@ (n - Most[Divisors[n]]), {n, 1, 40}] (* Ivan Neretin, May 26 2015 *)

for(n=1,40,d=divisors(n); print1(prod(j=1,matsize(d)[2]-1,n-d[j]),","))

a(n)=factorback(apply(d->if(dCharles R Greathouse IV, May 26 2015

a(n) = (n-d_1)(n-d_2)...(n-d_k) where d_k is the largest divisor of n less than n (k = tau(n) - 1).
a(p) = p-1, a(pq) = pq(p-1)(q-1)(pq-1), p and q prime.
If n is not a prime or the square of a prime then n divides a(n).

Edited and extended by Klaus Brockhaus, Jul 31 2002

A080498 a(n) = (n-c_1)(n-c_2)...(n-c_k) where c_k is the k-th composite number and is also the largest composite number < n.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 3, 8, 15, 48, 210, 1152, 3780, 19200, 62370, 322560, 2162160, 17418240, 81081000, 567705600, 2481078600, 16907304960, 146659312800, 1504935936000, 8799558768000, 76435881984000, 819678899239200

Offset: 1

Amarnath Murthy, Mar 19 2003

nonn

			a(6) = (6-4) = 2. a(10) = (10-4)(10-6)(10-8)(10-9) = 48.

Harvey P. Dale, Table of n, a(n) for n = 1..539

Cf. A080497, A072513, A080500.

Module[{nn=30,cmps},cmps=Select[Range[nn],CompositeQ];Table[Times@@(n-Select[ cmps,#Harvey P. Dale, Aug 13 2024 *)

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

A080500 a(n) = (n-1)(n-4)(n-9)...(n-k^2) where k^2 < n <= (k+1)^2.

Original entry on oeis.org

1, 1, 2, 3, 4, 10, 18, 28, 40, 54, 140, 264, 432, 650, 924, 1260, 1664, 4284, 8100, 13376, 20400, 29484, 40964, 55200, 72576, 93500, 236808, 443232, 728000, 1108380, 1603800, 2235968, 3028992, 4009500, 5206760, 6652800, 8382528, 20867704

Offset: 1

Amarnath Murthy, Mar 19 2003

nonn

The idea of A080497 to A080500 when applied to Euler's phi function i.e. on phi-torial function defined in A001783 yields A001783 itself for obvious reasons. Is there any other such example?

			a(6) = (6-1)(6-4)= 10.

Cf. A080497, A080498, A072513.

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

A275539 a(n) = n! + n*(n-1)!!.

Original entry on oeis.org

1, 2, 4, 12, 36, 160, 810, 5376, 41160, 366336, 3638250, 39959040, 479126340, 6227619840, 87180183090, 1307684044800, 20922822320400, 355687603568640, 6402374325997650, 121645103938928640, 2432902021271221500, 51090942249743155200, 1124000728080092512650

Offset: 0

Olivier Gérard, Aug 01 2016

Alois P. Heinz, Table of n, a(n) for n = 0..449

Cf. A000142, A080497.

a:= proc(n) option remember; `if`(n<5, [1, 2, 4, 12, 36]
      [n+1], ((n-3)^2*n*a(n-1) +(n-4)*n*(n-1)*a(n-2)
       -(n-3)*n*(n-1)*(n-2)*a(n-3))/((n-4)*(n-2)))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Dec 07 2016

Table[n! + n (n-1)!!, {n, 0, 20}] (* Bruno Berselli, Aug 11 2016 *)

a(n) = n! + n*(n-1)!! = n*((n-1)! + (n-1)!!).

cp's OEIS Frontend

A072513 Product of all n - d, where d < n and d is a divisor of n.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

PARI

Formula

Extensions

A080498 a(n) = (n-c_1)(n-c_2)...(n-c_k) where c_k is the k-th composite number and is also the largest composite number < n.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A080500 a(n) = (n-1)(n-4)(n-9)...(n-k^2) where k^2 < n <= (k+1)^2.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A275539 a(n) = n! + n*(n-1)!!.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Formula