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 A348203 #17 Dec 24 2024 07:31:10
%S A348203 1,2,3,5,5,9,7,11,11,15,11,20,13,21,21,23,17,31,19,32,29,33,23,42,29,
%T A348203 39,35,44,29,58,31,47,45,51,45,64,37,57,53,66,41,80,43,68,67,69,47,86,
%U A348203 55,83,69,80,53,97,69,90,77,87,59,119,61,93,91,95,81,124,67,104,93,126
%N A348203 a(n) = n - omega(n) + n * Sum_{p|n} 1/p.
%C A348203 For 1 <= k <= n, if k is a prime divisor of n then add n/k, otherwise add 1. For example, a(6) = 9 since the values of k from 1 to 6 would be: 1 + 6/2 + 6/3 + 1 + 1 + 1 = 9.
%C A348203 If p is prime, then a(p) = p since we have a(p) = p - omega(p) + phi(1)*omega(p/1) + phi(p)*omega(p/p) = p - 1 + 1*1 + (p-1)*0 = p.
%F A348203 a(n) = Sum_{k=1..n} (n/k)^(c(k) * (1 - ceiling(n/k) + floor(n/k))), where c is the prime characteristic (A010051).
%F A348203 a(n) = n - A001221(n) + A069359(n).
%F A348203 a(prime(n)) = prime(n).
%t A348203 Table[n - PrimeNu[n] + Sum[EulerPhi[k]*PrimeNu[n/k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]
%Y A348203 Cf. A000010 (phi), A001221 (omega), A010051, A069359.
%K A348203 nonn
%O A348203 1,2
%A A348203 _Wesley Ivan Hurt_, Oct 06 2021