login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A197410 Product of cumulative sums of divisors of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A032830 A225478

Adjacent sequences:  A197407 A197408 A197409 * A197411 A197412 A197413

KEYWORD

nonn,easy,nice

AUTHOR

Franklin T. Adams-Watters, Oct 14 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)