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 A344908 #32 Jun 23 2024 01:40:15
%S A344908 0,2,0,2,5,2,0,2,0,7,11,2,0,2,5,2,17,2,0,7,0,13,23,2,5,2,0,2,0,7,31,2,
%T A344908 11,19,5,2,0,2,0,7,41,2,0,13,5,25,47,2,0,7,17,2,0,2,16,2,0,2,59,7,0,
%U A344908 33,0,2,5,13,67,19,23,7,0,2,73,2,5,2,11,2,0,7,0,43,83,2,22
%N A344908 Sum of the distinct odd-indexed prime divisors, p_{2k-1}, of n.
%C A344908 a(m) = 0 for m in A066207. - _Michel Marcus_, Jun 12 2021
%C A344908 Inverse Möbius transform of n * c(n) * (pi(n) mod 2), where c(n) is the prime characteristic (A010051). - _Wesley Ivan Hurt_, Jun 23 2024
%H A344908 Martin Ehrenstein, <a href="/A344908/b344908.txt">Table of n, a(n) for n = 1..20000</a>
%F A344908 a(n) = Sum_{p|n} p * (pi(p) mod 2).
%F A344908 G.f.: Sum_{k>=1} prime(2*k-1) * x^prime(2*k-1) / (1 - x^prime(2*k-1)). - _Ilya Gutkovskiy_, Oct 24 2023
%F A344908 a(n) = Sum_{d|n} d * c(d) * (pi(d) mod 2), where c = A010051. - _Wesley Ivan Hurt_, Jun 23 2024
%e A344908 a(6) = Sum_{p|6} p * (pi(p) mod 2) = 2*(pi(2) mod 2) + 3*(pi(3) mod 2) = 2*1 + 3*0 = 2.
%t A344908 Table[Sum[k*Mod[PrimePi[k], 2] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
%o A344908 (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (primepi(f[k,1]) % 2, f[k,1])); \\ _Michel Marcus_, Jun 12 2021
%Y A344908 Cf. A000720 (pi), A008472 (sopf), A005074, A010051, A066207, A324966.
%Y A344908 Cf. A344931 (sum of distinct even-indexed prime divisors).
%K A344908 nonn
%O A344908 1,2
%A A344908 _Wesley Ivan Hurt_, Jun 02 2021