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A072513 Product of all n - d, where d < n and d is a divisor of n. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

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).

EXAMPLE

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.

MATHEMATICA

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

PROG

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

(PARI) a(n)=factorback(apply(d->if(d<n, n-d, 1), divisors(n))) \\ Charles R Greathouse IV, May 26 2015

(Haskell)

a072513 n = product $ map (n -) $ a027751_row n

-- Reinhard Zumkeller, May 27 2015

CROSSREFS

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

Cf. A027751.

Sequence in context: A126262 A258324 A080499 * A022404 A210420 A306585

Adjacent sequences:  A072510 A072511 A072512 * A072514 A072515 A072516

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jul 28 2002

EXTENSIONS

Edited and extended by Klaus Brockhaus, Jul 31 2002

STATUS

approved

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Last modified October 17 00:03 EDT 2019. Contains 328103 sequences. (Running on oeis4.)