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 A369171 #7 Jan 15 2024 09:42:33 %S A369171 3,11,17,19,43,51,59,62,67,74,83,89,91,97,99,115,123,124,131,139,146, %T A369171 149,155,163,170,174,187,188,197,203,206,211,219,227,233,235,241,259, %U A369171 267,274,278,279,283,291,293,305,307,314,331,337,339,341,342,347,349,350 %N A369171 Numbers k such that A000688(k) = A046660(k+1). %C A369171 The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 1, 15, 150, 1548, 15499, 154916, 1549105, 15489932, 154901767, 1549014294, ... . From these values the asymptotic density of this sequence, whose existence was proven by Erdős and Ivić (1987) (the constant c in the Formula section), can be empirically evaluated by 0.15490... . %D A369171 József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter XIII, p. 476. %H A369171 Amiram Eldar, <a href="/A369171/b369171.txt">Table of n, a(n) for n = 1..10000</a> %H A369171 Paul Erdős and Aleksandar Ivić, <a href="http://combinatorica.hu/~p_erdos/1987-32b.pdf">The distribution of values of a certain class of arithmetic functions at consecutive integers</a>, Colloq. Math. Soc. János Bolyai, 51, Number Theory, Budapest, 1987, pp. 45-91. See p. 60. %F A369171 The number of terms not exceeding x, N(x) = c * x + O(x^(3/4) * log(x)^4), where c > 0 is a constant (Erdős and Ivić, 1987). %t A369171 Select[Range[350], FiniteAbelianGroupCount[#] == PrimeOmega[#+1] - PrimeNu[#+1] &] %o A369171 (PARI) is(n) = vecprod(apply(numbpart, factor(n)[, 2])) == bigomega(n+1) - omega(n+1); %Y A369171 Cf. A000688, A046660. %K A369171 nonn,easy %O A369171 1,1 %A A369171 _Amiram Eldar_, Jan 15 2024