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 A351369 #13 Jul 16 2025 20:59:54
%S A351369 0,6,15,6,55,21,119,6,15,61,341,21,533,125,70,6,1003,21,1273,61,134,
%T A351369 347,1909,21,55,539,15,125,3161,76,3937,6,356,1009,174,21,5809,1279,
%U A351369 548,61,7339,140,8213,347,70,1915,9917,21,119,61,1018,539,12773,21,396,125,1288,3167
%N A351369 a(n) = Sum_{p|n, p prime} p * prime(p).
%C A351369 Inverse Möbius transform of n * prime(n) * c(n), where c(n) is the characteristic function of primes (A010051). - _Wesley Ivan Hurt_, Apr 01 2025
%H A351369 Harvey P. Dale, <a href="/A351369/b351369.txt">Table of n, a(n) for n = 1..1000</a>
%F A351369 a(n) = Sum_{d|n} d * prime(d) * c(d), where c = A010051. - _Wesley Ivan Hurt_, Apr 01 2025
%F A351369 a(p^k) = p * prime(p) for p prime and k>=1. - _Wesley Ivan Hurt_, Jul 16 2025
%e A351369 a(6) = 21; a(6) = Sum_{p|6} p * prime(p) = 2*3 + 3*5 = 21.
%t A351369 Join[{0},Table[Total[# Prime[#]&/@FactorInteger[n][[;;,1]]],{n,2,80}]] (* _Harvey P. Dale_, Jan 28 2024 *)
%Y A351369 Cf. A000040, A010051, A033286, A061397, A351368.
%K A351369 nonn
%O A351369 1,2
%A A351369 _Wesley Ivan Hurt_, Feb 08 2022