A197410 Product of cumulative sums of divisors of n.

1, 3, 4, 21, 6, 216, 8, 315, 52, 432, 12, 80640, 14, 720, 864, 9765, 18, 176904, 20, 232848, 1408, 1512, 24, 149299200, 186, 2016, 2080, 460992, 30, 274827168, 32, 615195, 2880, 3240, 3744, 13333320000, 38, 3960, 3808, 680400000, 42, 702079488, 44, 1270080

Offset: 1

Author

Franklin T. Adams-Watters, Oct 14 2011

Keywords

• nonn
• easy
• nice

Comments

When n is prime, a(n) = n + 1.

Examples

			a(4) = 21 because the divisors of 4 are 1, 2 and 4, their cumulative sums are 1, 3 and 7, and 1 * 3 * 7 = 21.
a(5) = 6 because the divisors of 5 are 1 and 5, their cumulative sums are 1 and 6, and 1 * 6 = 6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A007955, A064945.

Cf. A027750.

Programs

Haskell

a197410 = product . scanl1 (+) . a027750_row
-- Reinhard Zumkeller, Jan 26 2013

Mathematica

Table[Times@@Table[Plus@@Take[Divisors[n], k], {k, DivisorSigma[0, n]}], {n, 44}] (* Alonso del Arte, Oct 14 2011 *)
Table[Times@@Accumulate[Divisors[n]],{n,50}] (* Harvey P. Dale, Aug 15 2013 *)

PARI

a(n)=local(ds,sd);ds=divisors(n);prod(k=1,#ds,sd+=ds[k])