cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A197410 Product of cumulative sums of divisors of n.

This page as a plain text file.
%I A197410 #15 Aug 03 2014 14:37:24
%S A197410 1,3,4,21,6,216,8,315,52,432,12,80640,14,720,864,9765,18,176904,20,
%T A197410 232848,1408,1512,24,149299200,186,2016,2080,460992,30,274827168,32,
%U A197410 615195,2880,3240,3744,13333320000,38,3960,3808,680400000,42,702079488,44,1270080
%N A197410 Product of cumulative sums of divisors of n.
%C A197410 When n is prime, a(n) = n + 1.
%H A197410 Reinhard Zumkeller, <a href="/A197410/b197410.txt">Table of n, a(n) for n = 1..10000</a>
%e A197410 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.
%e A197410 a(5) = 6 because the divisors of 5 are 1 and 5, their cumulative sums are 1 and 6, and 1 * 6 = 6.
%t A197410 Table[Times@@Table[Plus@@Take[Divisors[n], k], {k, DivisorSigma[0, n]}], {n, 44}] (* _Alonso del Arte_, Oct 14 2011 *)
%t A197410 Table[Times@@Accumulate[Divisors[n]],{n,50}] (* _Harvey P. Dale_, Aug 15 2013 *)
%o A197410 (PARI) a(n)=local(ds,sd);ds=divisors(n);prod(k=1,#ds,sd+=ds[k])
%o A197410 (Haskell)
%o A197410 a197410 = product . scanl1 (+) . a027750_row
%o A197410 -- _Reinhard Zumkeller_, Jan 26 2013
%Y A197410 Cf. A000203, A007955, A064945.
%Y A197410 Cf. A027750.
%K A197410 nonn,easy,nice
%O A197410 1,2
%A A197410 _Franklin T. Adams-Watters_, Oct 14 2011