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 A020696 Let a,b,c,...k be all divisors of n; a(n) = (a+1)*(b+1)*...*(k+1). 5

%I

%S 2,6,8,30,12,168,16,270,80,396,24,10920,28,720,768,4590,36,31920,40,

%T 41580,1408,1656,48,2457000,312,2268,2240,104400,60,5499648,64,151470,

%U 3264,3780,3456,76767600,76,4680,4480,15343020,84,19071360,88

%N Let a,b,c,...k be all divisors of n; a(n) = (a+1)*(b+1)*...*(k+1).

%C a(p) = 2(p+1), a(p^2) = 2(p+1)(p^2+1) for primes p.

%H Reinhard Zumkeller, <a href="/A020696/b020696.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Product(A027750(n,k) + 1: k = 1..A000005(n)). - _Reinhard Zumkeller_, Mar 28 2015

%t Table[Times @@ (Divisors[n] + 1), {n, 43}] (* _Ivan Neretin_, May 27 2015 *)

%o (PARI) a(n) = {d = divisors(n); return (prod(i=1, #d, d[i]+1));} \\ _Michel Marcus_, Jun 12 2013

%o a020696 = product . map (+ 1) . a027750_row'

%o -- _Reinhard Zumkeller_, Mar 28 2015

%Y Cf. A027750, A000005, A003959.

%Y Cf. A057643 (LCM instead of product).

%Y Cf. A299436 (exp).

%K nonn,easy

%O 1,1

%A _Amarnath Murthy_, Jun 01 2003

%E Edited by _Don Reble_, Jun 05 2003

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Last modified May 19 02:29 EDT 2019. Contains 323377 sequences. (Running on oeis4.)