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.

A179215 Product of squarefree numbers less than n+1.

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%I A179215 #21 Sep 20 2021 04:58:29
%S A179215 1,1,2,6,6,30,180,1260,1260,1260,12600,138600,138600,1801800,25225200,
%T A179215 378378000,378378000,6432426000,6432426000,122216094000,122216094000,
%U A179215 2566537974000,56463835428000,1298668214844000,1298668214844000,1298668214844000,33765373585944000
%N A179215 Product of squarefree numbers less than n+1.
%H A179215 G. C. Greubel, <a href="/A179215/b179215.txt">Table of n, a(n) for n = 0..680</a>
%F A179215 a(n) = Product_{k=1..n} k^A008966(k).
%F A179215 A001221(a(n)) = A000720(n).
%F A179215 Subsequence of A025487.
%F A179215 A034386(n) <= a(n) <= A000142(n).
%F A179215 A179214(n) = a(2*n)/a(n-1) for n>0.
%p A179215 a:= proc(n) option remember; `if`(n=0, 1,
%p A179215       a(n-1)*`if`(issqrfree(n), n, 1))
%p A179215     end:
%p A179215 seq(a(n), n=0..27);  # _Alois P. Heinz_, Sep 20 2021
%t A179215 With[{sfnos=Select[Range[50],SquareFreeQ]},Table[Times@@Select[sfnos, #<n+1&],{n,0,30}]] (* _Harvey P. Dale_, Jun 13 2011 *)
%o A179215 (PARI) a(n) = prod(k=1, n, if (issquarefree(k), k, 1)); \\ _Michel Marcus_, Sep 20 2021
%o A179215 (PARI) a(n) = my(p=1); forsquarefree(x=1, n, p*=x[1]); p; \\ _Michel Marcus_, Sep 20 2021
%Y A179215 Cf. A013928, A066779, A005117, A008966, A179214.
%Y A179215 Cf. A000142, A000720, A001221, A025487, A034386.
%K A179215 nonn
%O A179215 0,3
%A A179215 _Reinhard Zumkeller_, Jul 05 2010
%E A179215 Definition corrected by _Harvey P. Dale_, Jun 13 2011