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.
%I A084893 #16 Feb 16 2025 08:32:50
%S A084893 1,1,8,6,9,2,4,6,1,9,7,2,7,6,4,2,8,4,6,2,6,1,6,6,9,9,3,8,1,3,7,1,1,8,
%T A084893 0,4,8,7,8,4,8,1,4,7,7,7,0,0,0,3,6,5,8,1,3,8,9,3,3,7,7,0,9,6,8,6,7,0,
%U A084893 8,1,5,0,4,4,2,7,8,9,8,5,9,2,1,6,1,1,1,9,0,1,8,3,4,1,2,8,9,5,3,9,5,7
%N A084893 Decimal expansion of Product_{j>=1, j!=3} zeta(j/3).
%C A084893 This constant, A_3, appears in the asymptotic formula A063966(n) = Sum_{k=1..n} A000688(k) = A_1 * n + A_2 * n^(1/2) + A_3 * n^(1/3) + O(n^(50/199 + e)), where e>0 is arbitrarily small, A_1 = A021002, and A_2 = A084892. - _Amiram Eldar_, Oct 16 2020
%D A084893 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 274.
%H A084893 B. R. Srinivasan, <a href="http://doi.org/10.4064/aa-23-2-195-205">On the Number of Abelian Groups of a Given Order</a>, Acta Arithmetica, Vol. 23, No. 2 (1973), pp. 195-205, <a href="https://eudml.org/doc/205185">alternative link</a>.
%H A084893 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AbelianGroup.html">Abelian Group</a>.
%e A084893 118.6924619727642846261669938137118...
%t A084893 m0 = 100; dm = 100; digits = 102; Clear[p]; p[m_] := p[m] = Zeta[1/3]*Zeta[2/3]*Product[Zeta[j/3], {j, 4, m}]; p[m0]; p[m = m0 + dm]; While[RealDigits[p[m], 10, digits + 10] != RealDigits[p[m - dm], 10, digits + 10], Print["m = ", m]; m = m + dm]; RealDigits[p[m], 10, digits] // First (* _Jean-François Alcover_, Jun 23 2014 *)
%o A084893 (PARI) prodinf(k=1, if (k!=3, zeta(k/3), 1)) \\ _Michel Marcus_, Oct 16 2020
%Y A084893 Cf. A000688, A021002, A063966, A084892.
%K A084893 nonn,cons
%O A084893 3,3
%A A084893 _Eric W. Weisstein_, Jun 10 2003