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 A362974 #7 Mar 24 2025 08:54:39
%S A362974 4,6,5,9,2,6,6,1,2,2,5,0,0,6,5,6,9,4,1,2,7,7,4,3,1,1,0,8,9,1,3,6,2,5,
%T A362974 8,6,2,1,3,0,5,4,3,3,6,7,2,8,3,2,5,6,5,3,8,4,7,5,7,6,9,2,4,0,1,5,3,0,
%U A362974 3,4,1,8,0,8,6,5,7,3,5,2,3,8,7,2,1,8,0,7,7,5,8,9,0,2,6,8,4,6,2,3,4,9,0,9,7
%N A362974 Decimal expansion of Product_{p prime} (1 + 1/p^(4/3) + 1/p^(5/3)).
%C A362974 The coefficient c_0 of the leading term in the asymptotic formula for the number of cubefull numbers (A036966) not exceeding x, N(x) = c_0 * x^(1/3) + c_1 * x^(1/4) + c_2 * x^(1/5) + o(x^(1/8)) (Bateman and Grosswald, 1958; Finch, 2003).
%D A362974 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 2.6.1, pp. 113-115.
%H A362974 Paul T. Bateman and Emil Grosswald, <a href="https://doi.org/10.1215/ijm/1255380836">On a theorem of Erdős and Szekeres</a>, Illinois Journal of Mathematics, Vol. 2, No. 1 (1958), pp. 88-98.
%H A362974 P. Shiu, <a href="https://doi.org/10.1017/S0017089500008351">The distribution of cube-full numbers</a>, Glasgow Mathematical Journal, Vol. 33, No. 3 (1991), pp. 287-295.
%H A362974 P. Shiu, <a href="https://doi.org/10.1017/S0305004100070705">Cube-full numbers in short intervals</a>, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 112, No. 1 (1992), pp. 1-5.
%F A362974 Equals 1 + lim_{m->oo} (1/m) Sum_{k=1..m} A337736(k).
%e A362974 4.65926612250065694127743110891362586213054336728325...
%t A362974 $MaxExtraPrecision = 1000; m = 1000; c = LinearRecurrence[{0, 0, 0, -1, -1}, {0, 0, 0, 4, 5}, m]; RealDigits[(1 + 1/2^(4/3) + 1/2^(5/3)) * (1 + 1/3^(4/3) + 1/3^(5/3)) * Exp[NSum[Indexed[c, n]*(PrimeZetaP[n/3] - 1/2^(n/3) - 1/3^(n/3))/n, {n, 4, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 120][[1]]
%o A362974 (PARI) prodeulerrat(1 + 1/p^4 + 1/p^5, 1/3)
%Y A362974 Cf. A036966, A090699 (analogous constant for powerful numbers), A244000, A337736, A362973, A362975 (c_1), A362976 (c_2).
%Y A362974 Cf. A051904.
%K A362974 nonn,cons
%O A362974 1,1
%A A362974 _Amiram Eldar_, May 11 2023