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 A377869 #29 Nov 19 2024 17:24:10 %S A377869 2,3,4,5,6,7,8,10,11,13,14,17,18,19,22,23,24,26,27,29,30,31,32,34,36, %T A377869 37,38,40,41,42,43,45,46,47,48,50,53,54,56,58,59,60,61,62,63,64,66,67, %U A377869 70,71,72,73,74,75,78,79,80,82,83,84,86,88,89,90,94,96,97,98,99,100,101,102,103,104,105,106,107,109 %N A377869 Numbers k such that A276085(k) has no divisors of the form p^p, where A276085 is fully additive with a(p) = p#/p. %C A377869 Numbers k for which A276085(k) is in A048103, i.e., in the range of A276086. %C A377869 Numbers k such that A276086(A276085(A276085(k))) is equal to A276085(k). %C A377869 This is a subsequence of A369003 (numbers k for which A276085(k) is not a multiple of 4), from which it differs for the first time at n=122, where a(122) = 175, as A369003(122) = 174 is not included in this sequence. %C A377869 From _Antti Karttunen_, Nov 17 2024: (Start) %C A377869 More generally, this is equal to setwise difference A000027 \ (A369002 U A377872 U A377878 U ...). %C A377869 Even semiprimes (A100484) is a subsequence, but the odd semiprimes (A046315) are all in the complement (A377873), because they are included in A369002. %C A377869 For k=1..6, there are 8, 70, 656, 6531, 64773, 645301 terms <= 10^k. Question: What is the asymptotic density of this sequence, if it has one? %C A377869 (End) %H A377869 Antti Karttunen, <a href="/A377869/b377869.txt">Table of n, a(n) for n = 1..10000</a> %H A377869 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a> %e A377869 A276085(11) = 210 = 2*3*5*7, which has no divisor of the form p^p, therefore 11 is included in this sequence. %e A377869 A276085(15) = 8 = 2^2 * 2, which has a divisor of the form p^p, therefore 15 is NOT included in this sequence. %e A377869 A276085(25) = 12 = 2^2 * 3, which has a divisor of the form p^p, therefore 25 is NOT included. %e A377869 A276085(34) = 30031 = A002110(1-1)+A002110(7-1) (as 34 = 2*17 = prime(1)*prime(7)), and because 30031 = 59*509 (an odd semiprime), 34 is included. %e A377869 A276085(60) = 10 = 2*5, which has no divisors of the form p^p, therefore 60 is included. %e A377869 A276085(102) = 30033 = 3^2 * 47 * 71, which has no p^p divisors, therefore 102 is included. %e A377869 A276085(174) = 223092873 = 3^3 * 3 * 1063 * 2591, which thus has a divisor of the form p^p, and therefore 174 is NOT included in this sequence. %o A377869 (PARI) \\ See A377868. %Y A377869 Cf. A046315, A048103, A276085, A276086, A377868 (characteristic function), A377873 (complement). %Y A377869 Setwise difference A369003 \ A377875. %Y A377869 Cf. A000040, A100484, A377871, A377989 (subsequences). %Y A377869 Cf. A369002, A377872, A377878. %K A377869 nonn %O A377869 1,1 %A A377869 _Antti Karttunen_, Nov 10 2024