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
Keywords
Examples
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.
Links
- Ivan Neretin, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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Haskell
a072513 n = product $ map (n -) $ a027751_row n -- Reinhard Zumkeller, May 27 2015
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Mathematica
Table[Times @@ (n - Most[Divisors[n]]), {n, 1, 40}] (* Ivan Neretin, May 26 2015 *) -
PARI
for(n=1,40,d=divisors(n); print1(prod(j=1,matsize(d)[2]-1,n-d[j]),","))
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PARI
a(n)=factorback(apply(d->if(d
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).
Extensions
Edited and extended by Klaus Brockhaus, Jul 31 2002
Comments