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.

A244285 Decimal expansion of A1*B1, the average number of non-isomorphic semisimple rings of any order, where A1 is Product_{m>1} zeta(m) and B1 is Product_{r*m^2 > 1} zeta(r*m^2).

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%I A244285 #18 Jan 31 2024 08:07:33
%S A244285 2,4,9,9,6,1,6,1,1,2,9,3,6,2,9,8,2,7,4,9,3,2,3,7,3,8,2,1,7,5,6,4,9,8,
%T A244285 0,3,4,5,7,0,4,0,2,2,5,8,8,0,7,5,9,5,4,4,3,2,0,6,2,1,0,9,4,8,1,2,1,2,
%U A244285 2,4,3,6,8,1,6,9,6,5,1,3,6,4,7,2,6,8,8,6,3,3,6,4,3,0,9,7,5,3,6,2,8,7,2,2,6
%N A244285 Decimal expansion of A1*B1, the average number of non-isomorphic semisimple rings of any order, where A1 is Product_{m>1} zeta(m) and B1 is Product_{r*m^2 > 1} zeta(r*m^2).
%C A244285 The asymptotic mean of A038538. - _Amiram Eldar_, Jan 31 2024
%D A244285 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, pp. 274-276.
%e A244285 2.499616112936298274932373821756498034570402258807595443206210948121224368...
%p A244285 Digits := 200: z:=product(Zeta(1.0*j), j = 2..1000): for k from 10 by 10 to 50 do print(z*product(product(Zeta(1.0*r*m^2), r = 1..k^2), m = 2..k)); end do; # _Vaclav Kotesovec_, Jun 11 2020
%t A244285 digits = 20; digitsPlus = 100; n0 = 50; dn = 1; A1 = NProduct[Zeta[m], {m, 2, Infinity}, WorkingPrecision -> digitsPlus]; Clear[B1]; B1[n_] := B1[n] = NProduct[Zeta[r*m^2], {r, 1, n}, {m, 2, n}, WorkingPrecision -> digitsPlus]; B1[n0]; B1[n = n0 + dn]; While[ RealDigits[B1[n], 10, digitsPlus] != RealDigits[B1[n - dn], 10, digitsPlus], Print["n = ", n]; n = n + dn]; RealDigits[A1*B1[n], 10, digits] // First
%o A244285 (PARI) prodinf(m = 2, zeta(m)) * prodinf(r = 1, prodinf(m = 2, zeta(r*m^2))) \\ _Amiram Eldar_, Jan 31 2024
%Y A244285 Cf. A021002 (A1), A038538, A123030.
%K A244285 nonn,cons
%O A244285 1,1
%A A244285 _Jean-François Alcover_, Jun 25 2014
%E A244285 More digits from _Vaclav Kotesovec_, Jun 11 2020