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 A084892 #21 Feb 16 2025 08:32:50
%S A084892 1,4,6,4,7,5,6,6,3,0,1,6,3,8,3,1,1,3,1,6,9,9,9,7,6,0,9,1,2,2,0,4,2,1,
%T A084892 9,2,6,3,8,1,1,7,3,0,3,4,7,9,6,9,6,0,2,5,1,6,9,2,6,9,3,9,7,5,2,0,1,2,
%U A084892 7,5,7,9,1,0,4,4,9,2,6,3,5,2,5,2,9,1,8,1,7,4,2,3,5,1,0,2,2,7,0,9,4,1
%N A084892 Decimal expansion of Product_{j>=1, j!=2} zeta(j/2) (negated).
%C A084892 This constant, A_2, 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_3 = A084893. - _Amiram Eldar_, Oct 16 2020
%D A084892 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 274.
%H A084892 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 A084892 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AbelianGroup.html">Abelian Group</a>.
%e A084892 -14.64756630163831131699976...
%t A084892 m0 = 100; dm = 100; digits = 102; Clear[p]; p[m_] := p[m] = Zeta[1/2]*Product[Zeta[j/2], {j, 3, 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 A084892 (PARI) prodinf(k=1, if (k!=2, zeta(k/2), 1)) \\ _Michel Marcus_, Oct 16 2020
%Y A084892 Cf. A000688, A021002, A063966, A084893.
%K A084892 nonn,cons
%O A084892 2,2
%A A084892 _Eric W. Weisstein_, Jun 10 2003