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

1,2

Comments

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

Links

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

Example

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.

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 *)

Prog

(PARI) a(n)=local(ds, sd); ds=divisors(n); prod(k=1, #ds, sd+=ds[k])
(Haskell)
a197410 = product . scanl1 (+) . a027750_row
-- Reinhard Zumkeller, Jan 26 2013

Crossrefs

Cf. A000203, A007955, A064945.

Cf. A027750.

Sequence in context: A069934 A206031 A206032 * A308689 A339482 A359883

Adjacent sequences: A197407 A197408 A197409 * A197411 A197412 A197413

Keyword

nonn,easy,nice

Author

Franklin T. Adams-Watters, Oct 14 2011

Status

approved