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 A336099 #39 Dec 10 2023 22:05:01 %S A336099 1,2,1,2,1,3,1,2,1,3,1,3,1,1,1,2,1,4,1,2,1,3,1,2,2,2,1,2,1,4,1,2,2,2, %T A336099 1,3,2,1,1,2,1,4,1,1,0,3,1,3,1,1,2,2,1,0,1,2,2,4,1,1,2,2,1,1,1,4,2,1, %U A336099 1,5,1,2,2,1,2,1,1,2,1 %N A336099 Number of solutions of the equation k = n*sopf(k) in positive integers where sopf(k) is the sum of distinct prime factors of k. %C A336099 Offset is 2 because a(1) cannot be defined since there are infinitely many solutions for n = 1, the primes. %C A336099 If n = p^s then p^(s+1) is solution of k = n*sopf(k). Hence a(p^s) > 0. On the other hand there are infinitely many 0's in the sequence. For example a(5^s*11^t) = 0 for all positive integers s, t. %C A336099 Records appear to occur only at prime n. These are seen in A336296, although note that A336296 is not monotonic, so it includes other terms. - _Bill McEachen_, Dec 02 2023 %H A336099 Vladimir Letsko, <a href="https://dxdy.ru/post1257616.html#p1257616">Mathematical Marathon, Problem 227</a> (in Russian). %e A336099 a(3) = 2 because there are exactly 2 solutions of the equation k = 3*sopf(k) in positive integers (9 and 30). %Y A336099 Cf. A008472, A336098, A336296. %Y A336099 Cf. A158804 (all possible k's). %K A336099 nonn %O A336099 2,2 %A A336099 _Vladimir Letsko_, Jul 08 2020