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 A329293 #12 Feb 16 2025 08:33:58
%S A329293 0,1,11,3,19,11,97,7,35,19
%N A329293 Number of positive integers k such that A002805(k) is not divisible by n, or a(n) = 0 if there are infinitely many such numbers.
%C A329293 There are two cases where a(n) = 0: (a) n divides A002805(k) for all k, which only happens for n = 1; (b) there are infinitely many k such that n does not divide A002805(k), which may happen for some primes p and their multiples.
%C A329293 For prime p and k >= p, A002805(k) is not divisible by p if and only if p divides A001008(floor(k/p)), which means a(p) mod p = p - 1.
%C A329293 If k == -1 or 0 (mod p), then p divides A001008(k) iff p^2 divides A001008(floor(k/p)), otherwise p divides A001008(k) iff p divides the numerator of (Sum_{i=floor(k/p)*p+1..k} 1/i) + (Sum_{i=1..floor(k/p)} 1/i)/p, where p is an odd prime and k >= p. See A329061 for more information.
%H A329293 Jinyuan Wang, <a href="/A329293/a329293_1.txt">PARI program and examples for n <= 10</a>
%H A329293 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%Y A329293 Cf. A001008, A002805, A329061.
%K A329293 nonn,more,hard
%O A329293 1,3
%A A329293 _Jinyuan Wang_, Dec 27 2019